Question

The difference between simple interest and compound interest on a certain sum is Rs. $54.40$ for $2$ years at $8$ percent per annum. Find the sum.

Answer 1

Given : $N=2years$ and $R=8$ %

We have $S.I.=\frac{PNR}{100}=\frac{P\times 2\times 8}{100}=\frac{16P}{100}=0.16P$

And on interest being compounded for $2$ years,

$Amount=P{(1+\frac{R}{100})}^N$

$=P{(1+\frac{8}{100})}^2$

$=P\times {\left(1.08\right)}^2=1.1664P$

$C.I.=A-P=1.1664P-P=0.1664P$

Given, $C.I.-S.I=Rs.54.40$

$\Rightarrow 0.1664P-0.16P=Rs.54.40$

$\Rightarrow 0.0064P=Rs.54.40$

$\Rightarrow P=Rs.8,500$