Question

A principal sum of money is lent out at compound interest compounded annually at the rate of 20% per annum for 2 years . It would give Rs 2410 more if the interest is compounded half year. Find the principal sum.

• A. Rs 120000
• B. Rs 125000
• C. Rs 100000
• D. Rs 110000

Answer 1

The correct option is C Rs 100000

Let the principal sum be Rs.x

Then Amount (at interest compounded annually)
$=x{(1+\frac{20}{100})}^2=\frac{36x}{25}$
Amount (at interest compounded half yearly)
$=x{(1+\frac{10}{100})}^4=\frac{14641x}{10000}$

Given $\frac{14641x}{10000}-\frac{36x}{25}=2410\Rightarrow \frac{14641x-14400x}{10000}=2410$
$\Rightarrow \frac{241x}{10000}=2410$

$\Rightarrow x=Rs.100000$