Suppose a person invested Rs. 15,000 in a mutual fund and the value of the investment at the time of redemption was Rs. 25,000. If CAGR % for this investment is 8.88%, then the number of years for which he has invested the amount is [ use : log 1.667 = 0.2219 ; log 1.089 = 0.0370]
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6
Let the amount be invested for n years. By the CAGR relation, the investment grows by the factor 1 + 0.0888 ≈ 1.089 each year:
\( \displaystyle 15000\,(1.089)^n=25000 \)
\( \displaystyle (1.089)^n=\frac{25000}{15000}=1.667 \)
Taking logarithms:
\( \displaystyle n\log 1.089=\log 1.667 \)
\( \displaystyle n=\frac{0.2219}{0.0370} \)
\( \displaystyle \approx 6 \)
CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate
