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Compound Interest
The difference between the amount and the money borrowed is called the compound interest for given period of time
1) Let principal =P; time =n years; and rate = r% per annum and let A be the total amount at the end of n years, then
A = P*[1+ (r/100)]n;
CI = {P*[1+ (r/100)]n -1}
2) When compound interest reckoned half yearly, then r% become r/2% and time n become 2n;
A= P*[1+ (r/2*100)]2n
3) For quarterly
A= P*[1+ (r/4*100)]4n
4) The difference between compound interest and simple interest over two years is given by
Pr2/1002or P(r/100)2
5) The difference between compound interest and simple interest over three years is given by
P(r/100)2*{(r/100)+3}
6) When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively, Then total amount is given by
P ((1 + R1)/100) ((1 + R2)/100) ((1 + R2)/100)
7) Present worth of Rs. x due n years hence is given by
x/(1+R/100)
1). Interest is compounded half-yearly, therefore,
Example:
Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the interest being compounded half-yearly.
Solution:
Principal = Rs. 20000, Rate = 2 % per half-year, Time = 2 years = 4 half- years
Amount=Rs.21648.64
Compound Interest = Total amount – Principal
= 21648.64 – 20000
= Rs. 1648.64
2). If interest is compounded annually,
Example:
Find compound interest on Rs. 8500 at 4 % per annum for 2 years, compounded annually.
Solution:
We are given:
Principal = Rs. 8500, Rate = 4 % per annum, Time = 2 years
Principal = Rs. 8500, Rate = 4 % per annum, Time = 2 years
= Rs. 9193.6
Compound Interest = Total amount – Principal
= 9193.6 – 8500
= 693.6
Compound Interest = Rs. 693.6
Compound Interest = Total amount – Principal
= 9193.6 – 8500
= 693.6
Compound Interest = Rs. 693.6
3). When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively. Then, Amount (= Principal + Compound interest) = P(1 + R1/100)(1 + R2/100)(1 + R3/100).
Example:
Find the compound interest on a principal amount of Rs.5000 after 2 years, if the rate of interest for the 1st year is 2% and for the 2nd year is 4%.
Solution:
Here R1 = 2% R2 = 4% and p = Rs.5000, we have to find CI (compound interest).
CI = 5000(1 + 2/100)(1 + 4/100) – 5000
= 5000 x (102/100)(104/100) – 5000
= 5000 x (51/50) x (52/50) – 5000
= 5000 x (51 x 52/2500) – 5000
= 5000 x (2652 / 2500) – 5000
= 5304 – 5000 = 304
Hence the required compound interest is Rs.304.
CI = 5000(1 + 2/100)(1 + 4/100) – 5000
= 5000 x (102/100)(104/100) – 5000
= 5000 x (51/50) x (52/50) – 5000
= 5000 x (51 x 52/2500) – 5000
= 5000 x (2652 / 2500) – 5000
= 5304 – 5000 = 304
Hence the required compound interest is Rs.304.
4). When compound interest is reckoned half-yearly.
If the annual rate is r% per annum and is to be calculated for n years, then in this case, rate = (n/2%) half-yearly and time = (2n) half-yearly.
Form the above we get
Example:
Sam investment Rs.15,000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be.
Solution:
P = Rs. 15000; R = 10% p.a = 5% half-year, T = 1 year = 2 half year
Amount = Rs
= Rs.16537.50
If the simple interest for certain sum for 2yrs at the annual rate of interest R% is SI. Then,
Compound interest (CI) = SI (1+r/200) (no. of years =2)
5). If the simple interest for a certain sum for 2 yr at 5%pa is 200, then what will be the compound interest for same sum for same period and the same rate of interest?
Sol:
Si =200 r=5%
Ci =200(1+5/200) =200*(205/200) =205
If a certain sum at compound interest becomes x times n1^yr and y times n2^yr then,
X1/N1 = Y1/N2
6). If an amount at compound interest becomes twice in 5yr, then in how many years, it will be 16 times at the same rate of interest?
21/5 = 16 1/x2
=24*1/x2
1/5 = 4/x2
X2 = 5*4 =20yrs
If a certain sum at compound interest amounts to A1 in n yrs and A2 in (n+1) yrs,
then
Rate of compound interest =(A2 – A1)/A1 *100%
Sum = A1 (A1 /A2)n
7). A sum of money invested at compound interest amounts to 800 in 2yr and 840 in 3yrs .Find the rate of interest and the sum.
A1 =800 ; A2 =840,
Rate of interest = (840-800)/800 *100% =40/8 =5%
Sum = 800 *(800/840)2 =320000/441 = Rs.725.62
If the populations of a city P and it increases with the rate of R% per annum, then
- Populations after n yr = p(1+R/100)n
- Populations n yr ago = p / (1+R/100)n
8). The population of a city A is 5000. It increases by 10% in 1st year. It decreases by 20% in the 2nd yr because of some reason. In the 3rd yr, the population increases by 30%. What will be the [population of area A at the end of 3yrs?
=5000(1+10/100)(1-20/100)(1+30/100)
= 500*(11/10)*(4/5)*(13/10) = 5720
Difference between ci and si 2yr =pr2 /1002
9). The difference between c.i and s.i for 2yr at the rate of 5% per annum is 5 .then the sum
5 = p (5/100)2 = Rs.2000
Rate of interest (no .of years =2)
(for only ci)
2% = 4.04%
3% = 6.09%
4% = 8. 16%
5% = 10.25%
6% = 12.36%
7% = 14.49%
8% = 16.64%
9% = 18.81%
10%= 20.00
+ 1.00 =21%
10). What is the Compound interest for Rs. 1500 at 5% rate of interest for 2 years?
1500*(10.25/100) =153.75
Difference between the compound interest and the simple interest
Example:
If the difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 3 years is Rs. 1220. What is the sum?
Solution:
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FAQs on Compound Interest - Quantitative Aptitude for Competitive Examinations - Banking Exams
| 1. What is compound interest? |  |
Compound interest is a financial concept where the interest earned on an initial investment or loan is added to the principal amount, and then the interest is calculated on the new total. This leads to exponential growth in the value of the investment or the amount owed over time.
| 2. How is compound interest different from simple interest? | |
Compound interest differs from simple interest in the way that the interest is calculated. In compound interest, the interest is calculated on the initial principal amount as well as the accumulated interest from previous periods. On the other hand, simple interest is calculated only on the initial principal amount.
| 3. How can I calculate compound interest? | |
To calculate compound interest, you need to know the initial principal amount, the interest rate, and the time period. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time period in years.
| 4. Can compound interest work against me? | |
Yes, compound interest can work against you if you have borrowed money or taken a loan. In this case, the interest added to the principal amount can quickly increase the total amount owed, especially if the interest rate is high and the loan repayment period is long. It is important to understand the terms and conditions of your loan to avoid getting trapped in a cycle of increasing debt.
| 5. How can I make the most of compound interest? | |
To make the most of compound interest, it is advisable to start saving or investing as early as possible. The longer the time period, the more significant the impact of compound interest. Additionally, choosing investments or savings accounts with higher interest rates or compounding frequencies can also maximize the growth of your money over time. Regularly contributing to your investments or savings can further enhance the benefits of compound interest.
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