Question

On what sum of money will compound interest (payable annually) for $2$ years be the same as simple interest on Rs. $9,430$ for $10$ years, both at the rate of $5$ per cent per annum?

Answer 1

For ,
$N=10years$
$R=5$ %
$P=Rs9,430$

We have $S.I.=\frac{PNR}{100}=\frac{9,430\times 10\times 5}{100}=Rs4,715$

And on interest being compounded for $2$ years and $R=5$ %, $Amount=P{(1+\frac{R}{100})}^N=P{(1+\frac{5}{100})}^2=P\times \left({\frac{21}{20}}^2\right)=\frac{441P}{400}$

So, $C.I.=A-P=\frac{441P}{400}-P=\frac{41P}{400}$

Given, $C.I.=S.I.$
$=>\frac{41P}{400}=Rs4,715$
$=>P=Rs46,000$