Question : A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a., compounded annually, and each instalment is INR 5,808, then the total interest charged in this scheme is:
Option 1: INR 1,563
Option 2: INR 1,536
Option 3: INR 1,632
Option 4: INR 1,602
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Correct Answer: INR 1,536
Solution :
Let the loan amount be P.
Then using
P = $\frac{\text{A}}{(1 +\frac{\text{r}}{100})^t}$, where A is amount due, $r$ = rate of interest, $t$ = years
⇒ P = $\frac{5808}{(1+\frac{10}{100})} + \frac{5808}{(1+\frac{10}{100})^{2}}$
= $\frac{5808}{\frac{11}{10}} + \frac{5808}{\frac{121}{100}}$
= $\frac{58080}{11} + \frac{580800}{121}$
= $5280 + 4800$
= $10080$
Now,
$\therefore$ Interest = (2 × instalment – P) = (2 × 5808 – 10080) = (11616 – 10080) = 1,536
Hence, the correct answer is INR 1,536.
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