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
Given: Principal $P = 15000$, Amount $A = 25000$, CAGR $r = 8.88\% = 0.0888$
CAGR formula: $A = P(1+r)^n$
$25000 = 15000(1.0888)^n$
$\frac{25000}{15000} = (1.0888)^n$
$1.667 = (1.0888)^n$
Take log on both sides: $\log 1.667 = n \log 1.0888$
$0.2220 = n \cdot 0.0370$
$n = \frac{0.2220}{0.0370} = 6$
Number of years = 6