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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.
Solution
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.
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