Question

Macro invested $8,201 into a fund that is expected to grow by 2.47% per year.How long will it take the fund to be worth double the amount invested? Round answer to the nearest whole number. Do not include the units.

Answer 1

Step 1

Given;

$\begin{gathered} Principal=8201 \\ r=2.47=\frac{2.47}{100}=0.0247 \end{gathered}$

Step 2

State the formula for if interest is compound

$A=P(1+\frac{r}{n})^{nt}$$\begin{gathered} A=8201\times2=\text{ \ }16402 \\ 16402=8201(1+\frac{0.0247}{1})^{1\times t} \\ \frac{16402}{8201}=\frac{8201(1+\frac{0.0247}{1})^{1\times t}}{8201} \\ 2=(1+\frac{0.0247}{1})^t \end{gathered}$$\begin{gathered} 2=(1.0247)^t \\ ln2=tln(1.0247) \\ t=\frac{ln2}{ln(1.0247)}=28.4078031 \\ t\approx28\text{ years} \end{gathered}$

Answer; Using interest compounded yearly the time taken for the amount to double is;

$28\text{ years to the nearest whole number}$