Question

A man borrowed some money and returned it in $3$ equal quarterly installments of Rs $4630.50$ each. Find the interest charged (in Rs) on the sum he borrowed, if the rate of interest was $20\%$ p.a. compounded quarterly?

• A. $1731.50$
• B. $1200$
• C. $1300$
• D. $1251.80$

Answer 1

The correct option is A $1731.50$

Here, we have to find present value $\left(V\right)$ of an ordinary annuity certain.

Given, $A=$ Rs $4630.50$, $n=3$

Also $r=\frac{20}{100}\times \frac{1}{4}=0.05$

$\therefore V=\frac{A}{r}\times [1-(1+r{)}^{(-n)}]=\frac{4630.50}{0.05}\times [1-\left(1.05{)}^{(-3)}\right]=$ Rs. $12610$

Thus, the sum borrowed was Rs. $12160$

Now, total money repaid $=3\times 4630.50=$ Rs. $13891.50$

Therefore, interest paid $=$ Rs, $13891.50$ $-$ Rs. $12160=$ Rs. $1731.50$.