Question

The simple interest on a sum of money for $3$ years at $\frac{20}{3}\%$ per annum is $Rs.8750$. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?

Answer 1

$SI=\frac{P\times R\times T}{100}$

$8750=\frac{P\times \frac{20}{3}\times 3}{100}$

$8750=\frac{20P}{100}$

$P=43750$

Compound Interest

$A=P(1+\frac{r}{100}{)}^t$

$=43750(1+\frac{\frac{20}{3}}{100}{)}^3$

$=43750(1+\frac{20}{3}\times \frac{1}{100}{)}^3$

$=43750(1+\frac{1}{15}{)}^3$

$=43750(\frac{16}{15}{)}^3$

$=43750\times \frac{16\times 16\times 16}{15\times 15\times 15}$

$=\frac{16\times 16\times 16\times 350}{3\times 3\times 3}$

$=\frac{4096\times 350}{27}$

$=\frac{1433600}{27}$

$=53096.296$

$=53096$

Compound Interest = A - P

$=53096-43750$

$=9346$ Answer.