Question

A sum of money is lent out at compound interest for two years at 20% per annum, compound interest being reckoned yearly. If the same sum of money was lent out at compound interest at the same rate per cent per annum, compound interest being reckoned half-yearly, it would have fetched Rs. 482 more by way of interest in two years. Calculate the sum of money lent out.

Answer 1

Let the sum of money lent out be Rs. x
In the Ist case:
$A_1=Rsx{(1+\frac{20}{100})}^2=Rs\frac{36x}{25}\therefore A=P{(1+\frac{r}{100})}^n$
In the 2nd case:
$A_2=Rsx{(1+\frac{20}{2\times 100})}^{2\times 2}=Rs.\frac{14641x}{10000}\because A=P{(1+\frac{r}{2\times 100})}^{n\times 2}$
Given, C.I. in the 2nd case is Rs. 482 more than the C.I. in the 1st case. $\Rightarrow$ For the same principal, amount in the 2nd case is Rs. 482 more than the amount in the 1st case.
$\Rightarrow \frac{14641x}{10000}-\frac{36x}{25}=482\Rightarrow x=20000$
$\therefore$ The sum of money lent out = Rs. 20,000