A person invested Rs. y in a mutual fund and the value of the investment at the time of redemption was Rs. \( x \). If he invested the amount for 3 years and the compound annual growth rate of his investment is 10%, then the value of \( \displaystyle\frac{y}{x} \) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1000}{1331} \)
With CAGR r over n years, the beginning value B and ending value E satisfy \( E=B(1+r)^n \).
Here B = y, E = x, r = 10% = 0.1 and n = 3:
\( \displaystyle x=y(1.1)^3=1.331\,y \)
\( \displaystyle \frac{y}{x}=\frac{1}{1.331}=\frac{1000}{1331} \)
Why the other options are incorrect
Option (2) \( \displaystyle\frac{1331}{1000} \) — Incorrect. \( \frac{1331}{1000} \) is \( \frac{x}{y} \), the ratio of the final value to the investment, turned the wrong way round.
Option (3) \( \displaystyle\frac{1331}{100} \) — Incorrect. \( \frac{1331}{100} \) is ten times \( \frac{x}{y} \), not \( \frac{y}{x} \).
Option (4) \( \displaystyle\frac{100}{1331} \) — Incorrect. \( \frac{100}{1331} \) is one-tenth of the correct value.