Question

If $3725 is invested at a rate of 5% compounded continuously, what will be the balance after 22 years? Round your answer to two decimal places.

Answer 1

To get the future balance after 22 years of compounding, we use the compound interest formula given below;

`\begin{gathered} A=P(1+r)^n \\ \text{where;} \\ A\text{ is the final balance or future balance after n-years} \\ P\text{ is the initial balance or principal} \\ r\text{ is the rate } \\ n\text{ is the number of years} \end{gathered}`

Given:

`\begin{gathered} P=\text{ \$3725} \\ r=5\text{ \%=}(5)/(100)=0.05 \\ n=22\text{years} \end{gathered}`

Substituting these values into the formula;

`\begin{gathered} A=P(1+r)^n \\ A=3725(1+0.05)^(22) \\ A=3725(1.05)^(22) \\ A=3725*1.05^(22) \\ A=10896.596 \\ \\ To\text{ two decimal places,} \\ A=\text{ \$10896.60} \end{gathered}`

Therefore, the balance after 22years to two decimal places would be $10,896.60