Question

Macro invested $7,161 into a fund that is expected to grow by 4.84% per year. Howlong will it take the fund to be worth double the amount invested? Round answer tothe nearest whole number.

Answer 1

Given:

$\begin{gathered} P=7,161 \\ r=4.84\% \\ A=2P \end{gathered}$

To Determine: How long it will take the fund to be worth double the amount

Solution

The formula for finding the amount for a compound interest is given as

$\begin{gathered} A=P(1+r)^t \\ A=Amount \\ P=Principal \\ r=rate \\ t=time \end{gathered}$

Substitute the given into the formula

$\begin{gathered} 2P=P(1+0.0484)^t \\ 2P=P(1.0484)^t \end{gathered}$$\begin{gathered} 1.0484^t=\frac{2P}{P} \\ 1.0484^t=2 \end{gathered}$$\begin{gathered} t\times ln(1.0484)=ln(2) \\ t=\frac{ln(2)}{ln(1.0484} \\ t=14.66506 \\ t\approx15years \end{gathered}$

Hence, the time it will the investment to be doubled is 15 years