Question

A sum of money, invested at compound interest, amounts to Rs. 19,360 in 2 years and to Rs. 23,425.60 in 4 years. Find the rate per cent and the original sum of money.

Answer 1

(for 2 years) A = Rs. 19360
T = 2 years
Let P = X

`"X"(1 + "R"/100)^2 = 19,360`                      ......(1)

A (for 4 years) = Rs. 23425.60

`"X"(1 + "R"/100)^4 = 23425.60`                   ......(2)

2 ÷ 1

`[ 1 + "R"/100]^2 = 23425.60/19360`

`[ 1 + "R"/100]^2 = 2342560/1936000`

`[ 1 + "R"/100]^2 = 14641/12100`

`[ 1 + "R"/100]^2 = [121/110]^2`

`1 + "R"/100 = 121/110`

`"R"/100 = 121/110 - 1`

R = 10%

From (1) x `[ 1 + 10/100 ]^2` = 19360

X = `[19360 xx 10 xx 10]/[11 xx 11]`

X = Rs. 16,000

Thus, sum = Rs. 16000