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प्रश्न
A person invests Rs5,000 for three years at a certain rate of interest compounded annually. At the end of two years this sum amounts to Rs6,272. Calculate :
(i) the rate of interest per annum.
(ii) the amount at the end of the third year.
उत्तर
Given: P = Rs. 5,000; A = Rs. 6,272 and n = 2 years.
(i) ∴ `"A" = "P"( 1 + r/100)^n`
⇒ `6,272 = 5,000( 1 + r/100 )^2`
⇒ `6,272/5,000 = ( 1 + r/100 )^2`
⇒ `784/625 = ( 1 + r/100 )^2`
⇒ `(28/25)^2 = ( 1 + r/100 )^2`
On comparing,
`28/25 = 1 + r/100`
On solving, we get
r = 12%
(ii) Amount at the third year
= `5,000( 1 + 12/100 )^3`
= `5000(28/25)^3`
= Rs. 7,024.64
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