Question

A sum of money is put at compound interest for 2 years at $20\%$ p.a. It would fetch ₹ 482 more, if the interest were payable half-yearly, than if it were payable yearly. The sum is

• A. ₹ 18000
• B. ₹ 20000
• C. ₹ 25000
• D. ₹ 23000

Answer 1

The correct option is B

₹ 20000

When the principal is compounded half-yearly
R = $\frac{R}{2}$ , n = $2\times 2$
Amount = $P(1+\frac{R}{100\times 2}{)}^4$
When the principal is compounded yearly
R = R, n = 2
Amount = $P(1+\frac{R}{100}{)}^2$
Hence,
$P[{(1+\frac{R}{100\times 2})}^{2\times 2}-{(1+\frac{R}{100})}^2]=482$
$\Rightarrow P[{(1+\frac{20}{100\times 2})}^4-{(1+\frac{20}{100})}^2]=482$
$\Rightarrow P\times 0.0241=482\Rightarrow p=₹20000$