Question

$Rs.20,000$ is lent for $2$ years at $5\%$ compound interest. Calculate the compound interest and the amount after $2$ years if the interest is compounded annually. What would have been the interest earned if the same amount was lent for simple interest at the same rate for the same duration?

Answer 1

Principal for the first year = $Rs.20,000$, rate = $5\%$, T = $1$ year.
Interest for the first year $=\frac{20,000\times 1\times 5}{100}=Rs.1,000$ (using simple interest formula $I=\frac{P\times T_1\times R}{100}$).
Principal for the second year = $Rs.20,000+1,000=Rs.21,000.$
Interest for the second year $=\frac{21,000\times 5}{100}=Rs.1,050$
Amount after 2 years = Rs. 21000 + 1050 = Rs. 22,050.
Compound interest = amount - principal = Rs. 22,050 - Rs. 20,000 = Rs. 2,050.
Hence the compound interest after 2 years is Rs. 2,050.
Simple interest on Rs. 20,000 for 2 years at the rate of 5% is
$I=\frac{20000\times 2\times 5}{100}=Rs.2,000$.