Question

A man borrowed some money and returned it in 3 equal quarterly installments of Rs 4630.50 each. What sum did he borrow if the rate of interest was 20% p.a. compounded quarterly?

• A. $12891.50$
• B. $12610$
• C. $13861.50$
• D. $13801.50$

Answer 1

The correct option is B $12610$

$\Rightarrow$ Here, $R=(20\times \frac{1}{4})\%=5\%$

$\Rightarrow$ Sum borrowed = $\frac{4630.50}{{(1+\frac{5}{100})}^1}+\frac{4630.50}{{(1+\frac{5}{100})}^2}+\frac{4630.50}{{(1+\frac{5}{100})}^3}$

$\Rightarrow$ Sum borrowed = $4630.50\times [\frac{100}{105}+\frac{(100{)}^2}{(105{)}^2}+\frac{(100{)}^3}{(105{)}^3}]$

$\Rightarrow$ Sum borrowed = $4630.50\times \frac{20}{21}\times [\frac{41}{21}+(\frac{20}{21}{)}^2]$

$\Rightarrow$ Sum borrowed = $4410\times \frac{1}{21}\times \frac{1261}{21}=Rs.12610$