Question

If the compound interest on a certain sum for two years at $10\%$ p.a. is Rs $3200$ and the simple interest on other Sum at the same rate for two years will be $12000$. What is the sum of the principal?

Answer 1

We know, compound interest $=$ Amount $-$ Principal
Therefore, $3200=P{(1+\frac{10}{100})}^2-P$
$\Rightarrow 3200=P(1.1{)}^2-P$
$\Rightarrow 1320=1.21P-P$
$\Rightarrow P=\frac{3200}{0.21}$
$\Rightarrow P=$ Rs. $15238$
Simple interest $=$ $\frac{PRT}{100}$
$\Rightarrow 12000=$ $\frac{P\times 10\times 2}{100}$
$\Rightarrow P=\frac{1000\times 100}{20}$
$\Rightarrow P=$ Rs. $60,000$
Sum of the principal $=15238+60000=$ Rs. $75238$