Question

The difference between the C.I. and S.I. on a sum of 7200 for two years is 72. Find the rate of interest per annum.

• A. $10\%$
• B. $12\%$
• C. $15\%$
• D. $20\%$

Answer 1

The correct option is A $10\%$

Simple Interest $SI=\frac{PNR}{100}$

So, $SI=\frac{7200\times 2\times R}{100}=Rs144R$
When interest is compounded, Amount $A=P(1+\frac{R}{100}{)}^n$

So, A $=7200\times (1+\frac{R}{100}{)}^2=Rs7200\times (1+\frac{R^2}{10000}+\frac{2R}{100})=Rs7200+Rs0.72R^2+Rs144R$

And $CI=A-P=Rs0.72R^2+Rs144R$
Si, difference $CI-SI=Rs0.72R^2+Rs144R-Rs144R=Rs72$

$0.72R^2=72$

$R^2=100$

So, $R=10$ %