If the interest on a sum of ₹y at 10% per annum compounded annually for 2 years is ₹462, then the total amount payable at the end…

Question

If the interest on a sum of ₹y at 10% per annum compounded annually for 2 years is ₹462, then the total amount payable at the end of the two-year period will be .

1. A. ₹2,762
2. B. ₹2,962
3. C. ₹2,662 (Correct answer)
4. D. ₹2,862

Correct Answer

Option C — ₹2,662

Detailed Solution & Explanation

The correct answer is ₹2,662.

Shortcut Trick

• For 2 years at $r\%$, compound interest is a fixed fraction of the principal: $\left[(1+r)^2 - 1\right]$. At 10% that is $1.21 - 1 = 0.21$, i.e. 21% of P.
• $0.21P = 462 \Rightarrow P = ₹2{,}200$.
• Amount $=$ principal $+$ interest $= 2200 + 462 = \textbf{₹2,662}$.

Alternate Method

• $A = P\left(1 + \dfrac{r}{100}\right)^n = P(1.1)^2 = 1.21P$
• $CI = A - P = 0.21P = 462 \Rightarrow P = 2200$
• $A = 1.21 \times 2200 = \textbf{₹2,662}$

Additional Information

• Two-year shortcuts worth memorising: at $r\%$, the two-year CI is $\left(2r + \dfrac{r^2}{100}\right)\%$ of the principal — at 10% that is $20 + 1 = 21\%$, matching above.
• CI always exceeds SI, and for 2 years the gap is exactly $P\left(\dfrac{r}{100}\right)^2$. Here $2200 \times 0.01 = ₹22$, so SI would be ₹440 against CI ₹462.
• The question asks for the amount, not the interest. Adding the interest back is the step most often missed under time pressure.