Ram had invested Rs. 15,000 in a mutual fund and the value of the investment at the time of redemption was Rs. 25,000. If the compound annual growth rate (CAGR) is 8.88%, then the number of years for which Ram has invested the amount is: [Given: \(\log 1.089 = 0.0370\) and \(\log 1.667 = 0.2220\)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 years
With a compound annual growth rate r over n years, the final value is
\(\text{Final value} = \text{Initial value} \times (1 + r)^n\)
\(25000 = 15000\,(1.0888)^n\)
\( \displaystyle (1.0888)^n = \frac{25000}{15000} = \frac{5}{3} \approx 1.667 \)
Taking logarithms, with 1.0888 rounded to 1.089 as in the given values:
\(n \log 1.089 = \log 1.667\)
\( \displaystyle n = \frac{0.2220}{0.0370} = 6 \)
So Ram invested the amount for 6 years.
CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate
