Question

The difference between the S.I. on a certain sum at the rate of 10% per annum for 2 years and C.I. which is compounded every 6 months is Rs. 124.05. What is the principal sum?

• A. Rs. 6000
• B. Rs. 8000
• C. Rs. 10,000
• D. Rs. 12,000

Answer 1

The correct option is B Rs. 8000

Let the sum=P Rs.
Rate of interest=10 %
Time=2 years.
$Simpleinterest=\frac{P\times 10\times 2}{100}=\frac{P}{5}$
Compound interest when it is calculated half yearly
$Compoundinterest=P{(1+\frac{5}{100})}^4-P=P{\left(\frac{21}{20}\right)}^4-P$
According to the question
$\Rightarrow P{\left(\frac{21}{20}\right)}^4-P-\frac{P}{5}=124.05$
$\Rightarrow P[{\left(\frac{21}{20}\right)}^4-1-\frac{1}{5}]=124.05$
$\Rightarrow P[\frac{194481}{160000}-1-\frac{1}{5}]=124.05$
$\Rightarrow P\left[\frac{194481-160000-32000}{160000}\right]=124.05$
$\Rightarrow P\left[\frac{2481}{160000}\right]=124.05$
$\Rightarrow P=\frac{124.05\times 160000}{2481}$
$\Rightarrow P=8000Rs.$