Question

The difference between compound interest and simple interest on a certain sum of money in 2 years at 4% per annum is Rs. 5,000. Find the principal amount

• A. Rs 30000
• B. Rs 31250
• C. Rs 32000
• D. Rs 32500
• E. None of the above

Answer 1

Answer: (E)

None of the above

$P$=principal; $n$=years and $r$= rate of interest

Given $n=2$ adn $r=2\%$

Also compound interest-Simple interest $=Rs.50,000$

$C.I=p\times {(1+\frac{r}{100})}^n-p=p{(1+\frac{4}{100})}^2-p$

$=p\left(\right(1+0.04{)}^2-1)$

$S.I=\frac{p\times n\times r}{100}=\frac{4\times 2\times p}{100}=0.08p$

Given $0.0816p=50,000+0.08p$

$\Rightarrow 0.0016p=50,000$

$\Rightarrow P=\frac{50,000}{0.0016}=31,250,000$