Question

The difference between S.I. and C.I. (compounded annually) on a sum of 64000 for 2 years is 1000. What is the rate of interest per annum?

• A. $25$%
• B. $16\frac{2}{3}\%$
• C. $13\frac{1}{3}\%$
• D. $12\frac{1}{2}\%$

Answer 1

The correct option is D $12\frac{1}{2}\%$

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

So, $SI=\frac{64000\times 2\times R}{100}=Rs1280R$
When interest is compounded, Amount $A=P(1+\frac{R}{100}{)}^n$

So, A $=64000\times (1+\frac{R}{100}{)}^2=Rs64000\times (1+\frac{R^2}{10000}+\frac{2R}{100})=Rs64000+Rs6.4R^2+Rs1280R$

And $CI=A-P=Rs6.4R^2+Rs1280R$
Si, difference $CI-SI=Rs6.4R^2+Rs1280R-Rs1280R=Rs1000$

$6.4R^2=1000$

$R^2=156.25$

So, $R=\frac{25}{2}$ % $=12\frac{1}{2}$ %