Question

A sum of money, invested at compound interest, amounts to Rs. 16,500 in 1 year and to Rs. 19,965 in 3 years. Find the rate per cent and the original sum of money invested.

Answer 1

Let sum of money be Rs P and rate of interest = r %
Money after 1 year = Rs. 16,500
Money after 3 years = Rs. 19,965

For 1 year
∴ `"A" = "P"( 1 + r/100 )^n`

⇒ 16,500 = P`( 1 + r/100 )^1`             ...(1)

For 3 years
∴  A = P`( 1 + r/100 )^n`
⇒ 19,965 = P`( 1 + r/100 )^3`             ...(2)

Divide eqⁿ (2) by eqⁿ (1)

`[19,965]/[ 16,500 ] = [P( 1 + r/100 )^3]/[P( 1 + r/100)^1]`

⇒ `121/100 = ( 1 + r/100 )^2`

⇒ `(11/10)^2 = ( 1 + r/100 )^2`

On comparing, we get

⇒ `11/10 = 1 + r/100 `

⇒ r = 10%

Put value of r in eqⁿ(1)
16,500 = P`( 1 + 10/100)`

⇒ P = `[16,500 xx 10]/11` = Rs. 15,000.