Question

Find the amount and the compound interest on Rs 5,000 at 5% per annum for one year if the interest is payable half-yearly.
(Solve without using formula)

Answer 1

Here, we calculate the compound interest for the period of one year in such a way that interest is calculated after six months. So, there will be two time intervals, each of six months, for the calculation of interest.
First Interval of Six Months
Interest on Rs 5000 for 6 months = $=\frac{5000\times 5\times 1}{2\times 100}=Rs125$

$\therefore$ Amount at the end of the first interval of six months
= Rs 5000 + Rs 125 = Rs 5125
Second Interval of Six Months
Amount at the end of the first interval of six months will be taken as the principal for the second interval of six months.
Interest on Rs 5125 for 6 months Rs $\frac{5125\times 5\times 1}{2\times 100}=Rs\frac{1025}{8}=Rs128.13$
$\therefore$ Total interest on Rs 5000 for one year = Rs 125 + Rs 128.13 = Rs 253.13.
Amount at the end of one year = Rs 5000 + Rs 253.13 = Rs 5253.13.