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=(2.47)/(100)=0.0247 \end{gathered}`

Step 2

State the formula for if interest is compound

`A=P(1+(r)/(n))^(nt)`
`\begin{gathered} A=8201*2=\text{ \$}16402 \\ 16402=8201(1+(0.0247)/(1))^(1* t) \\ (16402)/(8201)=(8201(1+(0.0247)/(1))^(1* t))/(8201) \\ 2=(1+(0.0247)/(1))^t \end{gathered}`
`\begin{gathered} 2=(1.0247)^t \\ ln2=tln(1.0247) \\ t=(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}`