### SIMPLE AND COMPOUND INTEREST

* Interest is the additional money paid for the usage of a certain amount.

* The amount borrowed is called the principal.

* The sum of interest and principal is called the amount.

Simple Interest

If the interest is calculated on same amount of money it is called the simple interest (S.I.).

Simple Interest will be the same for all the years.

If P is the principal, R is the rate of interest, T is time and S.I. the simple interest, then Note: Simple interest is always calculated on principal. Therefore simple interest is equal for every period.

e.g: 1. What would be the simple interest obtained on an a amount of Rs. 6850 at the rate of 6 p.c.p.a. after 3 years?

(A) Rs. 2423     (B) Rs. 1233     (C) Rs. 1633     (D) Rs. 1525    (E) None of these

Sol: Here P = Rs. 6850,     T= 3 years and     R = 6%  2. How long will it take for Rs. 1250 to become Rs. 1600 at 7% per annum simple interest?
(A) 5 years            (B) 3 years          (C) 4 years         (D) 6 years     (E) None of these
Sol: 3. What would be the amount on Rs. 8250 for 4 years at 15% per annum simple interest?

(A) Rs. 13200    (B) Rs. 12300   (C) Rs. 10450     (D) Rs. 11200   (E) None of these

SOl:  Shortcut: for one year, rate of interest is 15% and for 4 years it is 15×4 = 60% The Amount will become 160% If 100% Money = 8250, Compound Interest:

Interest which is calculated not only on the initial principal but also the accumulated interest of prior periods.

If A is the amount, C.I. is the compound interest, P is the principal, R is the rate, and T

is the time, then e.g: What is the compound interest accrued on an amount of Rs. 8000, at the rate of 6%
p.a. at the end of 2 years?
(A) Rs.2545     (B) Rs.2,257.20     (C) Rs.2986   (D) Rs.2775.40    (E) None of these
Sol:  Shortcut:  Amount = 106% of 106% 8000 =  8988.80
C.I. = 8988.80 - 8000 = Rs. 988.80
Note: 1. If the interest is paid half yearly, time is doubled and the rate is halved.
2. If the interest is paid quarterly, time becomes 4 times and the rate becomes onefourth

e.g: What is the interest accrued on Rs.12000 for one and half year at 4% p.a. compounded
half yearly? Difference between Simple and Compound Interest

Difference between Simple Interest and Compound Interest can be calculated by using formulae.

There is no difference between Simple and Compound Interest for one year. For 2 years  e.g: 1. What is the difference between Simple and Compound Interest for two years on Rs. 24000 at 7% rate?
Sol:  = Rs. 117.60
2. On what sum does the difference between Simple and Compound Interest for 3 years at 5% rate will be Rs. 244?

Sol:  Some other Models of Questions:

1. A sum of money will become Rs. 8060 in 4 years at 6% per annum simple interest. Find the sum.
Sol:  Shortcut: For one year, rate of interest is 6% and for 4 years it is 4 × 6% = 24% Then the amount will become 124%
If 124% money is Rs. 8060, 100% money will be × 8060 = Rs. 6500

2. Find the simple interest on Rs. 17500 at 7% per annum from August 5th to October 17th in the same year.

Sol: Time from August 5th to October 17th

=  26 days of August + 30 days of September and 17 days of October 3. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs. 72 more. What is that sum?

Sol: Interest for 2 years is Rs. 72. For one year it is Rs. 36
3% interest money is Rs. 72, then 100% money × 36 = Rs. 1200
Sum is Rs. 1200

4. A certain sum of money invested at compound interest doubles in 3 years. In how many years will it become 6 times itself?

Sol: Let the money be Rs. x It becomes Rs. 2x in 3 years As this is compound interest, 2x will be the principal for next period. Therefore, 2x will become 4x in next 3 years hence Rs. x will become 4x
i.e. 4 times in 3 + 3 = 6 years

5. A man deposits Rs. 12600 in a bank at 5% annual interest. After 8 months he withdraws Rs. 5400 together with interest and after 4 months the remaining money. How much does he get as interest at the end of the year?

Sol: S.I. of Rs. 12600 for 8 months He withdrew Rs. 5400 together with interest, the remaining amount
= 12600 - 5400 = Rs. 7200

S.I. on Rs. 7200 at the rate of 5% for 4 months Total interest = 420 + 120 = Rs. 540

Posted Date : 14-09-2021