Question

The compound interest in one year on a certain sum of money at $10\%$ per annum compounded half-yearly exceeds the simple interest on the same sum at the same rate and for the same period by Rs 30. Calculate the sum.

Answer 1

Let P be the principal
$CI=P(1+\frac{\frac{10}{2}}{100})=P(1.05{)}^2-P=P\times 1.1025-P=P\times 0.1025SI=\frac{P\times \text{/}10}{100}=P\times 0.1\therefore CI-SI=0.1025P-0.1P=0.0025P=30\therefore P=\frac{30}{0.0025}=\frac{300000}{25}=12000$
Sum is Rs 12000