A man invests 5000 for three years at a certain rate of interest compounded annually At the end of o...

Question

A man invests 5000 for three years at a certain rate of interest compounded annually At the end of one year it amounts to 5600 Calculate i the rate of interest per annum ii the interest accrued in the second year iii the amount at the end of the third year

Accepted Answer

Compound interest is calculated on the principal and interest accrued over a period of time. It differs from simple interest in that interest is not added to the principal when computing interest over time.

It is given that

Principal = ₹ 5000

Consider r% p.a. as the rate of interest

(i) We know that

At the end of one year

Interest = Prt/100

Substituting the values

= (5000 × r × 1)/ 100

= 50r

Here

Amount = 5000 + 50r

We can write it as

5000 + 50r = 5600

By further calculation

50r = 5600 – 5000 = 600

So we get

r = 600/50 = 12

Hence, the rate of interest is 12% p.a.

(ii) We know that

Interest for the second year = (5600 × 12 × 1)/ 100

= ₹ 672

So the amount at the end of the second year = 5600 + 672

= ₹ 6272

(iii) We know that

Interest for the third year = (6272 × 12 × 1)/ 100

= ₹ 752.64

So the amount after the third year = 6272 + 752.6

ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.1 in Chapter 2 - Compound Interest