Question

A person borrowed ₹15,000 from his friend at 5% per annum simple interest for 2 years. If he had borrowed this sum at 5% per annum compounded annually, what extra amount would he have to pay?

• A. ₹38.5
• B. ₹36.5
• C. ₹37.5
• D. ₹35.7

Answer 1

The correct option is C ₹37.5

Simple interest $=\frac{PTR}{100}$
$=\frac{15000\times 2\times 5}{100}$
$=150\times 2\times 5=₹1500$

Compount interest
$=P\times (1+\frac{R}{100}{)}^N-P$
$=15000\times (1+\frac{5}{100}{)}^2-15000$
$=15000\times (1+\frac{5}{100}{)}^2-15000$
$=15000\times (1+\frac{1}{20}{)}^2-15000$
$=15000\times (\frac{21}{20}{)}^2-15000$
$=15000\times \left(\frac{441}{400}\right)-15000$
$=15000\times (\frac{441}{400}-1)$
$=15000\times \left(\frac{41}{400}\right)$
$=37.5\times 41=₹1537.5$

C.I $-$ S.I $=1537.5-1500=₹37.5$

​​​​​​​The correct option is C.