Question

A sum of money becomes rs. 17280 in 2 years and rs. 20736 in 3 years at compound interest compounded annually. Find the sum.

Answer 1

Answer:

The required sum = Rs.12,000

Step-by-step explanation:

P = initial amount

R = rate of interest per cent per year (annual compounding)

T = time period in years

A = final amount at the end of T years

A = P(1 + R/100)^T

ATQ,

A = 17280 when T = 2

=> 17280 = P(1 + R/100)^2 .........Eqn 1

Also

A = 20736 when T = 3

=> 20736 = P(1 + R/100)^3 .........Eqn 2

Dividing Eqn 2 by Eqn 1, we get:

(20736/17280) = [(1 + R/100)^3] / [(1 + R/100)^2]

1.2 = (1 + R/100)

(1 + R/100) = 1.2

R/100 = 0.2

R = 20

Substituting for R in Eqn 1,

17280 = P(1 + 20/100)^2

17280 = P(1.2)^2

17280 = P(1.44)

P = 17280/1.44

P = 12000

The required sum is Rs.12,000 and the rate of interest = 20% per year