Question : A certain amount grows at an annual interest rate of 12% per annum, compounded monthly. Which of the following equations can be solved to find the number of years, $y$. That it would take for the investment to increase by a factor of 64?
Option 1: $64=(1.01)^{12y}$
Option 2: $\frac{1}{64}=(1.04)^{12y}$
Option 3: $64=(1.04)^{12y}$
Option 4: $8=(1.01)^{6y}$
Correct Answer: $64=(1.01)^{12y}$
Solution :
Given: Rate of interest = 12% per annual = 1% per month
Time = $12y$ months
Using the given formula,
Amount = P(1 + $\frac{R}{100})^n$, where P is principal, $R$ is the rate of interest per term for $n$ terms.
⇒ 64P = P(1 + $\frac{1}{100})^{12y}$
$\therefore 64=(1.01)^{12y}$
Hence, the correct answer is $64=(1.01)^{12y}$.
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