Question

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

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

Answer 1

The correct option is B Rs. 20000

$P[{(1+\frac{R}{100\times 2})}^{2\times 2}-{(1+\frac{R}{100})}^2]=482$
$\Rightarrow P[{(1+\frac{20}{100\times 2})}^4-{(1+\frac{20}{100})}^2]=482$
$\Rightarrow P(1.1{)}^4-(1.2{)}^2]=482$
$\Rightarrow P[1.4641-1.44]=482$

$\Rightarrow P\times 0.0241=482\Rightarrow p=Rs.20,000$