Question

The difference between simple interest and compound interest on a certain sum of money at the end of 2 years is Rs. 117 at 15% per annum, the interest being credited annually. The principal is-

• A. Rs. 5,200
• B. Rs. 5,980
• C. Rs. 6,760
• D. None of these.

Answer 1

The correct option is A Rs. 5,200

Let sum of money be ${}^{\prime }{P}^{\prime }$.

$r=15$%

$T=2$

$S.I=\frac{PTR}{100}$

$\Rightarrow S.I=\frac{P\times 2\times 15}{100}$

$C.I=P{(1+\frac{R}{100})}^T-P$

$=P{(1+\frac{15}{100})}^2-P$

$=P{\left(\frac{23}{20}\right)}^2-P$

$=\frac{129P}{400}$

ATP,

$\frac{129P}{400}-\frac{3P}{10}=117$

$\Rightarrow \frac{129P-120P}{400}=117$

$\Rightarrow 9P=117\times 400$

$\Rightarrow P=\frac{117\times 400}{9}=5200$

The principal is $Rs.5200$.