Simple Interest and Compound Interest Quant Notes | EduRev

Quantitative Aptitude for SSC CGL

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Quant : Simple Interest and Compound Interest Quant Notes | EduRev

The document Simple Interest and Compound Interest Quant Notes | EduRev is a part of the Quant Course Quantitative Aptitude for SSC CGL.
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Chapter - 19

SIMPLE INTEREST AND COMPOUND INTEREST

Principal is the amount on which interest is paid / earned.

If principal is denoted by P

The rate of interest is denoted by R

The time for which the principal is given on interest = T 

 Then

SIMPLE INTEREST 

Simple interest earned / paid is devoted by S.I.

Then (1) S.I. =Simple Interest and Compound Interest Quant Notes | EduRev
Simple Interest and Compound Interest Quant Notes | EduRev

Amount (A) = P + SI (Amount is the sum of P and the SI earned)

Amount x 100 = Principal x (100 + RT)

Principal = Simple Interest and Compound Interest Quant Notes | EduRev

 

COMPOUND INTEREST

Amount (A) = Simple Interest and Compound Interest Quant Notes | EduRev

Or CI = A – P

Difference of CI and SI for a period of one year in zero

For 2 years the difference of CI and SI is

Simple Interest and Compound Interest Quant Notes | EduRev

For 3 years the difference of CI and SI is

Simple Interest and Compound Interest Quant Notes | EduRev

  

SOLVED EXAMPLES

 Example 1: Ramesh deposited Rs. 29400 for 6 years at simple interest. After 6 years he received Rs. 4200 as interest. Find the annual rate of interest. 

  • P = Rs. 29400             T = 6 years        SI = Rs. 4200

For finding out the rate of interest R

Simple Interest and Compound Interest Quant Notes | EduRev

Example 2: I invested an amount of Rs. 17500 at the rate of 8% per annum. After how many years will I get Rs. 16800 as simple interest? 

  • P = Rs. 17500            R = 8%             SI = Rs.16800

So T = Simple Interest and Compound Interest Quant Notes | EduRev

So time is 12 years

 
Example 3: Pritam invested Rs. 16840 at 6% for 5 years. What amount of SI, he will get after 5 years. 

  • P = 16840

R = 6%

T = 5 years

Simple Interest and Compound Interest Quant Notes | EduRev = RS. 5052

Example 4: At what rate percent per annum simple interest a sum of money doubles itself in 15 years. 

  • let the principal be Rs. 100

T = 15 years

SI = Rs.100

R = ?

Simple Interest and Compound Interest Quant Notes | EduRev

Simple Interest and Compound Interest Quant Notes | EduRev

 Example 5: A sum of Rs. 3100 was lent partly at 5% and partly at 8% simple interest. The total interest received after 3 years was Rs. 600. Amount lent on 5% per annum was how much. 

  • let Rs. X be lent at 5%, then the remaining amount of Rs. (3100-x) was lent at 8%

SoSimple Interest and Compound Interest Quant Notes | EduRev

Or 15x + 24 (3100 – x) = 60000

Or 9x = 74400 – 60000

Simple Interest and Compound Interest Quant Notes | EduRev

SHORT CUT METHOD 

Let us suppose that whole amount was given at 5%

Interest = Simple Interest and Compound Interest Quant Notes | EduRev

But the interest earned in 600. It means some amount which earns Rs. 135 at 3% interest (8% - 5%) was given. This amount is

Simple Interest and Compound Interest Quant Notes | EduRev

So 3100 – 1500 = Rs. 1600 was given an interest of 5%.

 

Example 6: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent per annum. The rate per annum is what? 

  • Let the amount (Principal) be Rs. 1

SI = Rs. 4/9

Let rate be = x%

Then T = x years

As per the formula SI = PRT / 100

Simple Interest and Compound Interest Quant Notes | EduRev

Simple Interest and Compound Interest Quant Notes | EduRev

So rate per annum = Simple Interest and Compound Interest Quant Notes | EduRev

 

Example 7: In 4 years, the simple interest on a sum of money is 9/25 of the principal. Find out the annual rate of interest. 

  • Let the principal be Rs. 1

Interest = Simple Interest and Compound Interest Quant Notes | EduRev

T = 4 years

R =Simple Interest and Compound Interest Quant Notes | EduRev

Example 8: A sum of money at simple interest amounts to Rs. 1012 in 2½ years and to Rs. 1067.20 in 4 years. Find out the rate of interest, per year. 

Solution: From the question it is clear that

Rs. 1067.20 – Rs. 1012.00 = Rs. 55.20 is the simple interest earned in a period of 1½ years. So now we can find the interest earned in 2½ year which will be Simple Interest and Compound Interest Quant Notes | EduRev

= 18.40 x 5 = 92.00

So the principal in the beginning was Rs. 1012-92 = Rs. 920

So now P = Rs. 920

T = 5/2 year

Simple Interest = Rs. 92

Simple Interest and Compound Interest Quant Notes | EduRev

 

COMPOUND INTEREST 

To understand the method of calculating compound interest, let us consider an example.

Example: I borrowed Rs. 40,000 from a bank. The bank charges interest at the rate of 10% per annum. At the end of the year I will have to pay Rs.Simple Interest and Compound Interest Quant Notes | EduRev i.e. Rs. 4000 as interest.

Thus total amount of Rs. 40000 + Rs. 4000 = Rs. 44000 will have to be paid back to the bank.

If due to some reason I am not able to pay, the bank will charge 10% interest for the next year on the principal of Rs. 44000. At the end of the 2nd year the interest will be Rs.

Simple Interest and Compound Interest Quant Notes | EduRev = Rs. 4400.

Thus total interest payable to the bank will be Rs. (4400 + 4000) = Rs. 8400. This interest is Rs. 400 more than the simple interest on 40000 for 2 years at 10%. This Rs. 400 is the interest on the interest of 4000 for the first year. So the interest calculated in this way is called compound interest.

Remarks: For the first unit of time the simple and the compound interest are equal. From the second unit of time onwards the compound interest is more than the simple interest.

 

Example 1: find the compound interest on Rs. 3000 for 3 years at 8% per annum. 

  • Principal for the first year = Rs. 3000

Rate = 8%

Time = one year

Interest = Simple Interest and Compound Interest Quant Notes | EduRev = Rs. 240

Amount = Principal + interest = Rs. 3000 + 240 = Rs. 3240

 

Principal for 2nd year = Rs. 3240

Rate = 8%

Time = 1 year

So interest for 2nd year =  Simple Interest and Compound Interest Quant Notes | EduRev

So amount = Rs. 3240 + Rs. 259.20 = Rs. 3499.20

Principal for 3rd year = Rs. 3499.20

Rate = 8%

Time = 1 year

Interest for 3rd year = Simple Interest and Compound Interest Quant Notes | EduRev

So compound interest for 3 years

= Rs. 240 + Rs. 259.20 + Rs. 279.94 = Rs. 779.14

 

When interest is compounded half yearly.

Example 2: Find the compound interest on Rs. 1000 for 1½ year at 12% per annum when the interest is compounded half yearly.

  • Rate per annum is 12%

So the rate per half year will be 12/2 % or 6%. Also there will be 3 half years in 1½ year. By using the formula

Simple Interest and Compound Interest Quant Notes | EduRev

In this case P = 1000

r = 6% per half year

t = 3 half years

So A = Simple Interest and Compound Interest Quant Notes | EduRev

Simple Interest and Compound Interest Quant Notes | EduRev

So compound interest = Rs. 1191.02 – Rs. 1000 = Rs. 191.02

 

When the interest is compounded quarterly

 Example 3: Find the compound interest on Rs. 6000 for one year at 16% per annum when the interest is compounded quarterly. 

  • Rate per annum is 16%, so rate per quarter is 16/4 = 4%

Time is one year or 4 quarters

By the formula of compound interest

 Simple Interest and Compound Interest Quant Notes | EduRev

So compound interest for 4 quarters at the rate of 16% on 6000 is 7019.15 – 6000 = Rs. 1019.15

 

Example 4: At what rate per cent interest per annum, will Rs. 10000 amount to Rs. 14641 in 2 years. If the interest is compounded half yearly. 

  • Here P = Rs. 10000

A = Rs. 14641

R = ?

T = 2 years or 4 half years

Formula isA =  Simple Interest and Compound Interest Quant Notes | EduRev

or 14641 = Simple Interest and Compound Interest Quant Notes | EduRev

or  Simple Interest and Compound Interest Quant Notes | EduRev

Simple Interest and Compound Interest Quant Notes | EduRev

so 10% is half yearly rate

annual rate will be 10 x 2 = 20%

 

Example 5: The difference between the compound interest and simple interest on a certain sum at 14% per annum for 2 years is Rs. 147. Find the sum. 

  • Let the sum be Rs. 100

SI on 100 for 2 years at 14% is =Simple Interest and Compound Interest Quant Notes | EduRev

CI on 100 for 2 years at 14% = A – P

Simple Interest and Compound Interest Quant Notes | EduRev

Simple Interest and Compound Interest Quant Notes | EduRev

Difference in CI and SI =Simple Interest and Compound Interest Quant Notes | EduRev

If difference is Simple Interest and Compound Interest Quant Notes | EduRev = 100

If difference 1= Simple Interest and Compound Interest Quant Notes | EduRev

If difference is Rs. 147 = Simple Interest and Compound Interest Quant Notes | EduRev

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