Question

Find the difference between the compound interest (compounded annually) and the simple interest on $Rs2000$ for $3$ years at the rate of $8\%$ per annum.

Answer 1

Principal sum $P=Rs.2000$

Time period $\left(t\right)=3\text{years}$

Rate of interest $\left(R\right)=8\%$ per annum

As we know that,

$S.I.=\frac{P\times R\times t}{100}$

$\Rightarrow S.I.=\frac{2000\times 3\times 8}{100}=Rs.480$

Also,

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

$A=2000{(1+\frac{8}{100})}^3$

$\Rightarrow A=2000\times {\left(\frac{27}{25}\right)}^3$

$\Rightarrow A=Rs.2519.424$

Therefore,

$C.I.=A-P$

$\Rightarrow C.I.=2519.424-2000=Rs.519.424$

Now,

Difference between compound interest and simple interest $=519.424-480=Rs.39.424$