Question

Simple interest on a certain sum of money for $4$ years at $4$% per annum exceeds the compound interest on the same sum for $3$ years at $5$ per cent per annum by Rs. $228$. Find the sum.

Answer 1

For ,
$N=4years$
$R=4$ %

We have $S.I.=\frac{PNR}{100}=\frac{P\times 4\times 4}{100}=\frac{16P}{100}=0.16P$

And on interest being compounded for $3$ years and $R=5$ %, $Amount=P{(1+\frac{R}{100})}^N=P{(1+\frac{5}{100})}^3=P\times \left({1.05}^3\right)=1.157625P$

So, $C.I.=A-P=1.157625P-P=0.157625P$

Given, $S.I.-C.I=Rs228$
$=>0.16P-0.157625P=Rs228$
$=>0.002375P=Rs228$
$=>P=Rs96,000$