# Simple Interest

- The amount which is lent / deposited is called Principal
- The money that the principal generates is called Interest. This is the money generated as a result of borrowing/lending.
- Simple Interest is the interest calculated on the Principal amount, rather than being calculated on cumulative amount.
- Simple Interest, SI = P x R x T / 100, where P is the principal, R is the rate of interest per unit time period and T is the time period.
- Final Amount = Principal + SI

### Sample Problems

**Question 1 : **What would be the annual interest accrued on a deposit of Rs. 10,000 in a bank that pays 4 % per annum rate of simple interest ?

**Solution : **Here, P = 10000, R = 4, T = 1

=> SI = P x R x T / 100

=> SI = 10000 x 4 x 1 / 100

=> SI = 400

Thus, the annual interest would be Rs. 400

**Question 2 : **A sum of money amounts to Rs. 28,000 in 2 years at 20 % simple interest per annum. Find the sum.

**Solution : **Here, A = 28000, T = 2, R = 20

=> A = P + SI

=> A = P + (P x R x T / 100)

=> A = P [1 + (R x T / 100)]

=> 28000 = P [1 + 0.4]

=> P = 28000 / 1.4

=> P = 20000

Thus, the required sum is Rs. 20,000

**Question 3 : **A man borrowed a certain sum of money at the rate of 6 % per annum for the first two years , 9% per annum for the next three years, and 14% per annum for the period beyond 5 years. If he pays a total interest of Rs. 22,800 at the end of 9 years, find the amount he borrowed.

**Solution : **Let the borrowed sum be P.

=> SI for first 2 years + SI for next 3 years + SI for next 4 years = 22800

=> (P x 6 x 2 / 100) + (P x 9 x 3 / 100) + (P x 14 x 4 / 100) = 22800

=> 95 P / 100 = 22800

=> P = 24000

Therefore, Borrowed sum = Rs. 24,000

**Question 4 : **At what annual rate of interest will a sum of money be thrice in 10 years?

**Solution : **Amount = Principal + SI

If the sum of money would be thrice the principal after 10 years, the SI would be twice the principal.

=> SI = 2 x P

=> (P x R x T / 100) = 2 X P

=> R x T / 100 = 2

=> R x T = 200

=> R x 10 = 200

=> R = 20 %

Thus, the required rate of interest is 20 %

**Question 5 : **The simple interest on a sum of money in 5 years at 12 % per annum is Rs. 400 less than the simple interest accrued on the same sum in 7 years at 10 % per annum. Find the sum.

**Solution : **Let the sum be P.

=> SI in 5 years at 12 % per annum = P x 12 x 5 / 100 = 0.6 P

=> SI in 7 years at 10 % per annum = P x 10 x 7 / 100 = 0.7 P

Now, according to the question,

0.7 P – 0.6 P = 400

=> 0.1 P = 400

=> P = 4000

Thus, the required sum is Rs. 4000

**Question 6 : **A sum of Rs. 1000 was lent to two people, one at the rate of 5 % and other at the rate of 8 %. If the simple interest after one year is Rs. 62, find the sum lent at each rate.

**Solution : **Let the sum lent at 5 % be P.

=> Sum lent at 8 % = 1000 – P

Now, according to the question,

SI for 5 % + SI for 8 % = 62

=> (P x 5 x 1 / 100) + ((1000 – P) x 8 x 1 / 100) =62

=> 5 P + 8 (1000 – P) = 6200

=> 5 P + 8000 – 8 P = 6200

=> 3 P = 1800

=> P = 600

Therefore, sum lent at 5 % = P = Rs. 600

Sum lent at 8 % = 1000 – P = Rs. 400

### Problems on Simple Interest | Set-2

This article has been contributed by **Nishant Arora**

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