NCERT Textbook: Concepts & Modes of Analysis | Financial Literacy for Class 10 PDF Download

 Page 1


CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
Introduction to Financial Markets
51
Page 2


CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
Introduction to Financial Markets
51
CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
50
Page 3


CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
Introduction to Financial Markets
51
CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
50
Thus,
S = Rs. 10,000[1+0.075(5)] 
= Rs. 13,750
Here, the simple interest earned is Rs. 3,750.
A comparison of the interest amounts calculated under both the method indicates that Mr. X 
would have earned Rs.749.48 (Rs. 4,499.48 - Rs. 3,750) or nearly 20% more under the compound 
interest method than under the simple interest method.
Simply put, compounding refers to the re-investment of income at the same rate of return to 
constantly grow the principal amount, year after year. Should one care too much whether the 
rate of return is 5% or 15%? The fact is that with compounding, the higher the rate of return, 
more is the income which keeps getting added back to the principal regularly generating higher 
rates of return year after year.
The table below shows you how a single investment of Rs. 10,000 will grow at various rates of 
return with compounding. 5% is what you might get by leaving your money in a savings bank 
account, 10% is typically the rate of return you could expect from a one-year company fixed 
deposit, 15% - 20% or more is what you might get if you prudently invest in mutual funds or 
equity shares.
The Impact of Power of Compounding:
The impact of the power of compounding with different rates of return and different time 
periods:
At end of Year 5% 10% 15% 20%
1 Rs 10500 Rs 11000 Rs 11500 Rs 12000
5 Rs 12800 Rs 16100 Rs 20100 Rs 24900
10 Rs 16300 Rs 25900 Rs 40500 Rs 61900
15 Rs 20800 Rs 41800 Rs 81400 Rs 154100
25 Rs 33900 Rs 1,08300 Rs 3,29200 Rs 9,54,000
Money has time value. The idea behind time value of money is that a rupee now is worth more 
than rupee in the future. The relationship between value of a rupee today and value of a rupee in 
future is known as ‘Time Value of Money’. A rupee received now can earn interest in future. An 
amount invested today has more value than the same amount invested at a later date because it 
can utilize the power of compounding. Compounding is the process by which interest is earned 
on interest. When a principal amount is invested, interest is earned on the principal during the 
first period or year. In the second period or year, interest is earned on the original principal plus 
the interest earned in the first period. Over time, this reinvestment process can help an amount 
to grow significantly.
What is meant by the Time Value of Money?
Let us take an example:
Suppose you are given two options:
(A) Receive Rs. 10,000 now    or
(B) Receive Rs. 10,000 after three years.
Which of the options would you choose?
Rationally, you would choose to receive the Rs.10,000 now instead of waiting for three years to 
get the same amount. So, the time value of money demonstrates that, all things being equal, it is 
better to have money now rather than later.
Back to our example: by receiving Rs.10,000 today, you are poised to increase the future value of 
your money by investing and gaining interest over a period of time. For option B, you don’t have 
time on your side, and the payment received in three years would be your future value. To 
illustrate, we have provided a timeline:
If you are choosing option A, your future value will be Rs.10,000 plus any interest acquired over 
the three years. The future value for option B, on the other hand, would only be Rs. 10,000. This 
clearly illustrates that value of money received today is worth more than the same amount 
received in future since the amount can be invested today and generate returns.
Let us take an another example:
If you choose option A and invest the total amount at a simple annual rate of 5%, the future 
value of your investment at the end of the first year is Rs. 10,500, which is calculated by 
multiplying the principal amount of Rs.10,000 by the interest rate of 5% and then adding the 
interest gained to the principal amount.
Thus, Future value of investment at end of first year:
= ((Rs.10,000 X (5/100)) + Rs.10,000
= (Rs.10,000 X 0.050) + Rs.10,000
= Rs.10,500
You can also calculate the total amount of a one-year investment with a simple modification of 
the above equation:
Original equation: (Rs.10,000 x 0.050) + Rs.10,000 = Rs.10,500
Modified formula: Rs.10,000 x [(1 x 0.050) + 1] = Rs.10,500
Final equation: Rs. 10,000 x (0.050 + 1) = Rs. 10,500
0 1 2 3 Years
Future Value Present Value
Option A : Rs. 10,000 Rs. 10,000 + Interest
Option B : Rs. 10,000 Rs. 10,000
Introduction to Financial Markets
53
Page 4


CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
Introduction to Financial Markets
51
CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
50
Thus,
S = Rs. 10,000[1+0.075(5)] 
= Rs. 13,750
Here, the simple interest earned is Rs. 3,750.
A comparison of the interest amounts calculated under both the method indicates that Mr. X 
would have earned Rs.749.48 (Rs. 4,499.48 - Rs. 3,750) or nearly 20% more under the compound 
interest method than under the simple interest method.
Simply put, compounding refers to the re-investment of income at the same rate of return to 
constantly grow the principal amount, year after year. Should one care too much whether the 
rate of return is 5% or 15%? The fact is that with compounding, the higher the rate of return, 
more is the income which keeps getting added back to the principal regularly generating higher 
rates of return year after year.
The table below shows you how a single investment of Rs. 10,000 will grow at various rates of 
return with compounding. 5% is what you might get by leaving your money in a savings bank 
account, 10% is typically the rate of return you could expect from a one-year company fixed 
deposit, 15% - 20% or more is what you might get if you prudently invest in mutual funds or 
equity shares.
The Impact of Power of Compounding:
The impact of the power of compounding with different rates of return and different time 
periods:
At end of Year 5% 10% 15% 20%
1 Rs 10500 Rs 11000 Rs 11500 Rs 12000
5 Rs 12800 Rs 16100 Rs 20100 Rs 24900
10 Rs 16300 Rs 25900 Rs 40500 Rs 61900
15 Rs 20800 Rs 41800 Rs 81400 Rs 154100
25 Rs 33900 Rs 1,08300 Rs 3,29200 Rs 9,54,000
Money has time value. The idea behind time value of money is that a rupee now is worth more 
than rupee in the future. The relationship between value of a rupee today and value of a rupee in 
future is known as ‘Time Value of Money’. A rupee received now can earn interest in future. An 
amount invested today has more value than the same amount invested at a later date because it 
can utilize the power of compounding. Compounding is the process by which interest is earned 
on interest. When a principal amount is invested, interest is earned on the principal during the 
first period or year. In the second period or year, interest is earned on the original principal plus 
the interest earned in the first period. Over time, this reinvestment process can help an amount 
to grow significantly.
What is meant by the Time Value of Money?
Let us take an example:
Suppose you are given two options:
(A) Receive Rs. 10,000 now    or
(B) Receive Rs. 10,000 after three years.
Which of the options would you choose?
Rationally, you would choose to receive the Rs.10,000 now instead of waiting for three years to 
get the same amount. So, the time value of money demonstrates that, all things being equal, it is 
better to have money now rather than later.
Back to our example: by receiving Rs.10,000 today, you are poised to increase the future value of 
your money by investing and gaining interest over a period of time. For option B, you don’t have 
time on your side, and the payment received in three years would be your future value. To 
illustrate, we have provided a timeline:
If you are choosing option A, your future value will be Rs.10,000 plus any interest acquired over 
the three years. The future value for option B, on the other hand, would only be Rs. 10,000. This 
clearly illustrates that value of money received today is worth more than the same amount 
received in future since the amount can be invested today and generate returns.
Let us take an another example:
If you choose option A and invest the total amount at a simple annual rate of 5%, the future 
value of your investment at the end of the first year is Rs. 10,500, which is calculated by 
multiplying the principal amount of Rs.10,000 by the interest rate of 5% and then adding the 
interest gained to the principal amount.
Thus, Future value of investment at end of first year:
= ((Rs.10,000 X (5/100)) + Rs.10,000
= (Rs.10,000 X 0.050) + Rs.10,000
= Rs.10,500
You can also calculate the total amount of a one-year investment with a simple modification of 
the above equation:
Original equation: (Rs.10,000 x 0.050) + Rs.10,000 = Rs.10,500
Modified formula: Rs.10,000 x [(1 x 0.050) + 1] = Rs.10,500
Final equation: Rs. 10,000 x (0.050 + 1) = Rs. 10,500
0 1 2 3 Years
Future Value Present Value
Option A : Rs. 10,000 Rs. 10,000 + Interest
Option B : Rs. 10,000 Rs. 10,000
Introduction to Financial Markets
53
Thus,
S = Rs. 10,000[1+0.075(5)] 
= Rs. 13,750
Here, the simple interest earned is Rs. 3,750.
A comparison of the interest amounts calculated under both the method indicates that Mr. X 
would have earned Rs.749.48 (Rs. 4,499.48 - Rs. 3,750) or nearly 20% more under the compound 
interest method than under the simple interest method.
Simply put, compounding refers to the re-investment of income at the same rate of return to 
constantly grow the principal amount, year after year. Should one care too much whether the 
rate of return is 5% or 15%? The fact is that with compounding, the higher the rate of return, 
more is the income which keeps getting added back to the principal regularly generating higher 
rates of return year after year.
The table below shows you how a single investment of Rs. 10,000 will grow at various rates of 
return with compounding. 5% is what you might get by leaving your money in a savings bank 
account, 10% is typically the rate of return you could expect from a one-year company fixed 
deposit, 15% - 20% or more is what you might get if you prudently invest in mutual funds or 
equity shares.
The Impact of Power of Compounding:
The impact of the power of compounding with different rates of return and different time 
periods:
At end of Year 5% 10% 15% 20%
1 Rs 10500 Rs 11000 Rs 11500 Rs 12000
5 Rs 12800 Rs 16100 Rs 20100 Rs 24900
10 Rs 16300 Rs 25900 Rs 40500 Rs 61900
15 Rs 20800 Rs 41800 Rs 81400 Rs 154100
25 Rs 33900 Rs 1,08300 Rs 3,29200 Rs 9,54,000
Money has time value. The idea behind time value of money is that a rupee now is worth more 
than rupee in the future. The relationship between value of a rupee today and value of a rupee in 
future is known as ‘Time Value of Money’. A rupee received now can earn interest in future. An 
amount invested today has more value than the same amount invested at a later date because it 
can utilize the power of compounding. Compounding is the process by which interest is earned 
on interest. When a principal amount is invested, interest is earned on the principal during the 
first period or year. In the second period or year, interest is earned on the original principal plus 
the interest earned in the first period. Over time, this reinvestment process can help an amount 
to grow significantly.
What is meant by the Time Value of Money?
Let us take an example:
Suppose you are given two options:
(A) Receive Rs. 10,000 now    or
(B) Receive Rs. 10,000 after three years.
Which of the options would you choose?
Rationally, you would choose to receive the Rs.10,000 now instead of waiting for three years to 
get the same amount. So, the time value of money demonstrates that, all things being equal, it is 
better to have money now rather than later.
Back to our example: by receiving Rs.10,000 today, you are poised to increase the future value of 
your money by investing and gaining interest over a period of time. For option B, you don’t have 
time on your side, and the payment received in three years would be your future value. To 
illustrate, we have provided a timeline:
If you are choosing option A, your future value will be Rs.10,000 plus any interest acquired over 
the three years. The future value for option B, on the other hand, would only be Rs. 10,000. This 
clearly illustrates that value of money received today is worth more than the same amount 
received in future since the amount can be invested today and generate returns.
Let us take an another example:
If you choose option A and invest the total amount at a simple annual rate of 5%, the future 
value of your investment at the end of the first year is Rs. 10,500, which is calculated by 
multiplying the principal amount of Rs.10,000 by the interest rate of 5% and then adding the 
interest gained to the principal amount.
Thus, Future value of investment at end of first year:
= ((Rs.10,000 X (5/100)) + Rs.10,000
= (Rs.10,000 X 0.050) + Rs.10,000
= Rs.10,500
You can also calculate the total amount of a one-year investment with a simple modification of 
the above equation:
Original equation: (Rs.10,000 x 0.050) + Rs.10,000 = Rs.10,500
Modified formula: Rs.10,000 x [(1 x 0.050) + 1] = Rs.10,500
Final equation: Rs. 10,000 x (0.050 + 1) = Rs. 10,500
0 1 2 3 Years
Future Value Present Value
Option A : Rs. 10,000 Rs. 10,000 + Interest
Option B : Rs. 10,000 Rs. 10,000
52
Page 5


CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
Introduction to Financial Markets
51
CONCEPTS & MODES OF ANALYSIS
Chapter 9
What is Simple Interest?
What is Compound Interest?
Simple Interest: Simple Interest is the interest paid only on the principal amount borrowed. No 
interest is paid on the interest accrued during the term of the loan.
There are three components to calculate simple interest: principal, interest rate and time.
Formula for calculating simple interest:
I = Prt
Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
Example:
Mr. X borrowed Rs. 10,000 from the bank to purchase a household item. He agreed to repay the 
amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of Rs.  10,000 in eight months, the interest would be:
P = Rs. 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be:
I = Rs. 10,000*(0.10)*(8/12) = Rs. 667.
This is the Simple Interest on the Rs. 10,000 loan taken by Mr. X for 8 months.
If he repays the amount of Rs. 10,000 in fifteen months, the only change is with time.
Therefore, his interest would be:
I = Rs. 10,000*(0.10)*(15/12) = Rs. 1,250
Compound Interest: Compound interest means that, the interest will include interest calculated 
on interest. The interest accrued on a principal amount is added back to the principal sum, and 
the whole amount is then treated as new principal, for the calculation of the interest for the next 
period.
For example, if an amount of Rs. 5,000 is invested for two years and the interest rate is 10%, 
compounded yearly:
At the end of the first year the interest would be (Rs. 5,000 * 0.10) or Rs. 500.
In the second year the interest rate of 10% will applied not only to Rs. 5,000 but also to the 
Rs. 500 interest of the first year. Thus, in the second year the interest would be (0.10 * Rs. 
5,500) or Rs. 550.
¦
¦
For any loan or borrowing unless simple interest is stated, one should always assume interest is 
compounded. When compound interest is used we must always know how often the interest rate 
is calculated each year. Generally the interest rate is quoted annually. E.g. 10% per annum.
Compound interest may involve calculations for more than once a year, each using a new 
principal, i.e. (interest+principal). The first term we must understand in dealing with compound 
interest is conversion period. Conversion period refers to how often the interest is calculated 
over the term of the loan or investment. It must be determined for each year or fraction of a year.
E.g.: If the interest rate is compounded semiannually, then the number of conversion periods per 
year would be two. If the loan or deposit was for five years, then the number of conversion 
periods would be ten.
Formula for calculating Compound Interest:
n
C = P (1+i)
Where
C = amount
P = principal
i = Interest rate per conversion period
n = total number of conversion periods
Example:
Mr. X invested Rs. 10,000 for five years at an interest rate of 7.5% compounded quarterly
P = Rs.10,000
i = 0.075/4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years
Therefore, the amount, C, is: 
C = Rs.10,000(1 + 0.01875) ^20 
= Rs.10,000 x 1.449948 
= Rs.14,499.48
So at the end of five years Mr. X would earn Rs.4,499.48 (Rs.14,499.48 -Rs.10,000) as interest. 
This is also called as Compounding.
Compounding plays a very important role in investment since earning a simple interest and 
earning an interest on interest makes the amount received at the end of the period for the two 
cases significantly different.
If Mr. X had invested this amount for five years at the same interest rate offering the simple 
interest option, then the amount that he would earn is calculated by applying the following 
formula:
S = P (1 + rt)
P = 10,000 
r = 0.075 
t = 5
50
Thus,
S = Rs. 10,000[1+0.075(5)] 
= Rs. 13,750
Here, the simple interest earned is Rs. 3,750.
A comparison of the interest amounts calculated under both the method indicates that Mr. X 
would have earned Rs.749.48 (Rs. 4,499.48 - Rs. 3,750) or nearly 20% more under the compound 
interest method than under the simple interest method.
Simply put, compounding refers to the re-investment of income at the same rate of return to 
constantly grow the principal amount, year after year. Should one care too much whether the 
rate of return is 5% or 15%? The fact is that with compounding, the higher the rate of return, 
more is the income which keeps getting added back to the principal regularly generating higher 
rates of return year after year.
The table below shows you how a single investment of Rs. 10,000 will grow at various rates of 
return with compounding. 5% is what you might get by leaving your money in a savings bank 
account, 10% is typically the rate of return you could expect from a one-year company fixed 
deposit, 15% - 20% or more is what you might get if you prudently invest in mutual funds or 
equity shares.
The Impact of Power of Compounding:
The impact of the power of compounding with different rates of return and different time 
periods:
At end of Year 5% 10% 15% 20%
1 Rs 10500 Rs 11000 Rs 11500 Rs 12000
5 Rs 12800 Rs 16100 Rs 20100 Rs 24900
10 Rs 16300 Rs 25900 Rs 40500 Rs 61900
15 Rs 20800 Rs 41800 Rs 81400 Rs 154100
25 Rs 33900 Rs 1,08300 Rs 3,29200 Rs 9,54,000
Money has time value. The idea behind time value of money is that a rupee now is worth more 
than rupee in the future. The relationship between value of a rupee today and value of a rupee in 
future is known as ‘Time Value of Money’. A rupee received now can earn interest in future. An 
amount invested today has more value than the same amount invested at a later date because it 
can utilize the power of compounding. Compounding is the process by which interest is earned 
on interest. When a principal amount is invested, interest is earned on the principal during the 
first period or year. In the second period or year, interest is earned on the original principal plus 
the interest earned in the first period. Over time, this reinvestment process can help an amount 
to grow significantly.
What is meant by the Time Value of Money?
Let us take an example:
Suppose you are given two options:
(A) Receive Rs. 10,000 now    or
(B) Receive Rs. 10,000 after three years.
Which of the options would you choose?
Rationally, you would choose to receive the Rs.10,000 now instead of waiting for three years to 
get the same amount. So, the time value of money demonstrates that, all things being equal, it is 
better to have money now rather than later.
Back to our example: by receiving Rs.10,000 today, you are poised to increase the future value of 
your money by investing and gaining interest over a period of time. For option B, you don’t have 
time on your side, and the payment received in three years would be your future value. To 
illustrate, we have provided a timeline:
If you are choosing option A, your future value will be Rs.10,000 plus any interest acquired over 
the three years. The future value for option B, on the other hand, would only be Rs. 10,000. This 
clearly illustrates that value of money received today is worth more than the same amount 
received in future since the amount can be invested today and generate returns.
Let us take an another example:
If you choose option A and invest the total amount at a simple annual rate of 5%, the future 
value of your investment at the end of the first year is Rs. 10,500, which is calculated by 
multiplying the principal amount of Rs.10,000 by the interest rate of 5% and then adding the 
interest gained to the principal amount.
Thus, Future value of investment at end of first year:
= ((Rs.10,000 X (5/100)) + Rs.10,000
= (Rs.10,000 X 0.050) + Rs.10,000
= Rs.10,500
You can also calculate the total amount of a one-year investment with a simple modification of 
the above equation:
Original equation: (Rs.10,000 x 0.050) + Rs.10,000 = Rs.10,500
Modified formula: Rs.10,000 x [(1 x 0.050) + 1] = Rs.10,500
Final equation: Rs. 10,000 x (0.050 + 1) = Rs. 10,500
0 1 2 3 Years
Future Value Present Value
Option A : Rs. 10,000 Rs. 10,000 + Interest
Option B : Rs. 10,000 Rs. 10,000
Introduction to Financial Markets
53
Thus,
S = Rs. 10,000[1+0.075(5)] 
= Rs. 13,750
Here, the simple interest earned is Rs. 3,750.
A comparison of the interest amounts calculated under both the method indicates that Mr. X 
would have earned Rs.749.48 (Rs. 4,499.48 - Rs. 3,750) or nearly 20% more under the compound 
interest method than under the simple interest method.
Simply put, compounding refers to the re-investment of income at the same rate of return to 
constantly grow the principal amount, year after year. Should one care too much whether the 
rate of return is 5% or 15%? The fact is that with compounding, the higher the rate of return, 
more is the income which keeps getting added back to the principal regularly generating higher 
rates of return year after year.
The table below shows you how a single investment of Rs. 10,000 will grow at various rates of 
return with compounding. 5% is what you might get by leaving your money in a savings bank 
account, 10% is typically the rate of return you could expect from a one-year company fixed 
deposit, 15% - 20% or more is what you might get if you prudently invest in mutual funds or 
equity shares.
The Impact of Power of Compounding:
The impact of the power of compounding with different rates of return and different time 
periods:
At end of Year 5% 10% 15% 20%
1 Rs 10500 Rs 11000 Rs 11500 Rs 12000
5 Rs 12800 Rs 16100 Rs 20100 Rs 24900
10 Rs 16300 Rs 25900 Rs 40500 Rs 61900
15 Rs 20800 Rs 41800 Rs 81400 Rs 154100
25 Rs 33900 Rs 1,08300 Rs 3,29200 Rs 9,54,000
Money has time value. The idea behind time value of money is that a rupee now is worth more 
than rupee in the future. The relationship between value of a rupee today and value of a rupee in 
future is known as ‘Time Value of Money’. A rupee received now can earn interest in future. An 
amount invested today has more value than the same amount invested at a later date because it 
can utilize the power of compounding. Compounding is the process by which interest is earned 
on interest. When a principal amount is invested, interest is earned on the principal during the 
first period or year. In the second period or year, interest is earned on the original principal plus 
the interest earned in the first period. Over time, this reinvestment process can help an amount 
to grow significantly.
What is meant by the Time Value of Money?
Let us take an example:
Suppose you are given two options:
(A) Receive Rs. 10,000 now    or
(B) Receive Rs. 10,000 after three years.
Which of the options would you choose?
Rationally, you would choose to receive the Rs.10,000 now instead of waiting for three years to 
get the same amount. So, the time value of money demonstrates that, all things being equal, it is 
better to have money now rather than later.
Back to our example: by receiving Rs.10,000 today, you are poised to increase the future value of 
your money by investing and gaining interest over a period of time. For option B, you don’t have 
time on your side, and the payment received in three years would be your future value. To 
illustrate, we have provided a timeline:
If you are choosing option A, your future value will be Rs.10,000 plus any interest acquired over 
the three years. The future value for option B, on the other hand, would only be Rs. 10,000. This 
clearly illustrates that value of money received today is worth more than the same amount 
received in future since the amount can be invested today and generate returns.
Let us take an another example:
If you choose option A and invest the total amount at a simple annual rate of 5%, the future 
value of your investment at the end of the first year is Rs. 10,500, which is calculated by 
multiplying the principal amount of Rs.10,000 by the interest rate of 5% and then adding the 
interest gained to the principal amount.
Thus, Future value of investment at end of first year:
= ((Rs.10,000 X (5/100)) + Rs.10,000
= (Rs.10,000 X 0.050) + Rs.10,000
= Rs.10,500
You can also calculate the total amount of a one-year investment with a simple modification of 
the above equation:
Original equation: (Rs.10,000 x 0.050) + Rs.10,000 = Rs.10,500
Modified formula: Rs.10,000 x [(1 x 0.050) + 1] = Rs.10,500
Final equation: Rs. 10,000 x (0.050 + 1) = Rs. 10,500
0 1 2 3 Years
Future Value Present Value
Option A : Rs. 10,000 Rs. 10,000 + Interest
Option B : Rs. 10,000 Rs. 10,000
52
Which can also be written as:
S = P (r+ 1)
Where,
S = amount received at the end of period
P = principal amount
r = interest rate (per year)
This formula denotes the future value (S) of an amount invested (P) at a simple interest of (r) for 
a period of 1 year.
The time value of money may be computed in the following circumstances:
1. Future value of a single cash flow
2. Future value of an annuity
3. Present value of a single cash flow
4. Present value of an annuity
1. Future Value of a Single Cash Flow
For a given present value (PV) of money, future value of money (FV) after a period M:’ for 
which compounding is done at an interest rate of V , is given by the equation
t
FV  = PV (1+r)
This assumes that compounding is done at discrete intervals. However, in case of 
continuous compounding, the future value is determined using the formula
r t
FV = PV * e
Where ‘e’ is a   mathematical function called  ‘exponential’ the  value  of exponential 
(e) = 2.7183. The compounding factor is calculated by taking natural logarithm (log to the 
base of 2.7183).
Example 1: Calculate the value of a deposit of Rs. 2,000 made today, 3 years hence if the 
interest rate is 10%.
By discrete compounding:
3 3
FV = 2,000 * (1+0.10) = 2,000 * (1.1) = 2,000 * 1.331 = Rs. 2,662
By continuous compounding:
10 3
FV = 2,000 * e ( ) =2,000 * 1.349862 = Rs.2699.72
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° *
2. Future Value of an Annuity
An annuity is a stream of equal annual cash flows. The future value (FVA) of a uniform 
cash flow (CF) made at the end of each period till the time of maturity ‘t’ for which 
compounding is done at the rate V is calculated as follows:
How is time value of money computed?
t–1 t–2 1
FVA = CF* (1+r) + CF* (1+r) + ... + CF* (1+r) + CF
= CF
t
(1+r) –1
r
amount after a certain period, to know how much to save annually to reach the targeted 
amount, to know the interest rate etc.
Example 1: Suppose, you deposit Rs.3,000 annually in a bank for 5 years and your deposits 
earn a compound interest rate of 10 per cent, what will be value of this series of deposits 
(an annuity) at the end of 5 years?  Assume that each deposit occurs at the end of the year.
Future value of this annuity is:
4 3 2
= Rs.3000*(1.10) + Rs.3000*(1.10)  + Rs.3000*(1.10) + Rs.3000*(1.10) + Rs.3000
= Rs.3000*(1.4641)+Rs.3000*(1.3310)+Rs.3000*(1.2100)+Rs.3000*(1.10)+ Rs.3000
= Rs. 18315.30
3. Present Value of a Single Cash Flow
Present value of (PV) of the future sum (FV) to be received after a period T for which 
discounting is done at an interest rate of V , is given by the equation
1
In case of discrete discounting: PV = FV / (1+r)
Example 1: What is the present value of Rs.5,000 payable 3 years hence, if the interest rate 
is 10 % p.a.
3 _ r t
PV = 5000/ (1.10) i.e. = Rs.3756.57 In case of continuous discounting:   PV = FV * e
Example 2: What is the present value of Rs. 10,000 receivable after 2 years at a discount 
rate of 10% under continuous discounting? 
Present Value = 10,000/(exp ^(0.1*2)) = Rs. 8187.297
4.   Present Value of an Annuity
The present value of annuity is the sum of the present values of all the cash inflows of this 
annuity.
Present value of an annuity (in case of discrete discounting) 
1 1
PVA = FV [{(1+r) – 1 }/ {r * (1+r) }]
The term [ is referred as the Present Value Interest factor for an annuity 
(PVIFA).
Present value of an annuity (in case of continuous discounting) is calculated as:
– r t
PV = FV * (1–e )/r
a a
Example 1:   What is the present value of Rs. 2000/- received at the end of each year for 3 
continuous years
= 2000*[1/1.10]+2000*[1/1.10] ^2+2000*[1/1.10] ^3
= 2000*0.9091+2000*0.8264+2000*0.7513
= 1818.181818+1652.892562+1502.629602
= Rs. 4973.704
(FVIFA). The same can be applied in a variety of contexts. For e.g. to know accumulated 
t t
(1+r) –1/r* (1+r) )] 
The term
t
(1+r) –1
r
is referred as the Future Value Interest factor for an annuity
Introduction to Financial Markets
55