A man borrows ₹ 2550 to be paid back with compound interest at the rate of 4\% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?
(a)₹ 1275
(b)₹ 1283
(c)₹ 1352
(d)₹ 1377
Answer
Answer (as printed): C
Explanation
Let the value of each instalment be ₹ $x$. Then, (P.W. of ₹ $x$ due 1 year hence) $$\begin{aligned} & \quad+(\text { P.W. of ₹ } x \text { due 2 years hence })=₹ 2550 \\ & \Leftrightarrow \frac{x}{\left(1+\frac{4}{100}\right)}+\frac{x}{\left(1+\frac{4}{100}\right)^{2}}=2550 \\ & \Leftrightarrow \frac{25 x}{26}+\frac{625 x}{676}=2550 \\ & \Leftrightarrow 1275 x=2550 \times 676 \\ & \Leftrightarrow x=\left(\frac{2550 \times 676}{1275}\right)=1352 . \end{aligned}$$ ∴ Value of each instalment $=₹ 1352$.
Explanation as extracted from the printed page; notation may be imperfect.