Question

On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180/-. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.

Answer 1

P=?
R=10%
CI-SI=Rs 180
$SI=\frac{PRT}{100}$
$=10\times \frac{1P}{100}=\frac{P}{10}$ ..........................(i)
$CI=P(1+\frac{R}{200}{)}^2-P$ ... payable half yearly
$CI=P\times (\frac{210}{200}{)}^2-P$
$CI=\frac{441P}{400}-P$
$CI=\frac{41P}{400}$...........................(ii)
$Diff.=CI-SI=\frac{41P}{400}-\frac{P}{10}=\frac{P}{400}$
But, given, diff.= 180
Therefore,
$180=\frac{P}{400}$
$\therefore P=Rs72000$