Question

A sum of money was lent for 2 years at $20\%$ compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs. 482 more. Find the sum.

Answer 1

Let Sum (P) = Rs. x
Rate (R) $=20\%$ p.a or $10\%$ half-yearly
Period (n) = 2 years or 4 half years
In first case,
$A=P{(1+\frac{R}{100})}^n$
$=Rs.100{(1+\frac{20}{100})}^2=Rs.100{\left(\frac{6}{5}\right)}^2$
$=Rs.100\times \frac{6}{5}\times \frac{6}{5}=Rs.144$
$\therefore$ C.I = A - P = Rs. 144 - Rs. 100 = Rs. 44
In second case,
$A=P{(1+\frac{R}{100})}^n=Rs.100{(1+\frac{10}{100})}^4$
$=Rs.100\times \frac{6}{5}\times \frac{6}{5}=Rs.144$
$\therefore$ C.I = A - P = Rs. 144 - Rs. 100 = Rs. 44
In second case,
$A=P{(1+\frac{R}{100})}^n=Rs.100{(1+\frac{10}{100})}^4$
$=Rs.100{\left(\frac{11}{10}\right)}^4$
$=Rs.100\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}$
$=Rs.\frac{14641}{100}=Rs.146.41$
$\therefore$ Interests = A - P = Rs. 146.41 - Rs. 100
$=Rs.46.41$
Now difference in interests
= Rs. 46.41 - Rs. 44.00 = Rs. 2.41
If difference is 2.41 then sum is 100
If difference is Rs. 482, then sum
$=\frac{100}{2.41}\times 482=\frac{100\times 100\times 482}{241}$
$=Rs.20,000$