Question

A sum of money is invested at $10\%$ per annum compounded half-yearly. If the difference of the amounts at the end of 6 months and 12 months is Rs 189, find the sum of money invested.

Answer 1

Let the sum invested = P
$r=10\%pa$
Compoundary - half yearly
$\therefore$ Amount at the end of 6 months $P(1+\frac{5}{100})12=P(1+\frac{5}{100}{)}^2$
$Difference=P(1+\frac{5}{100}{)}^2-P(1+\frac{5}{100})$
$=P(1+\frac{5}{100})P(\text{/}1+\frac{5}{100})=P(1+\frac{5}{100})\left(\frac{5}{100}\right)=Rs189\therefore P=\frac{{}^{\text{/}9}{}^{\text{/}63}18\times \text{/}{100}^{20}\times \text{/}{100}^{20}}{\text{/}{165}_{\text{/}{35}_{\text{/}5}}\times \text{/}5}=9\times 400=Rs3600$