Question

Carl Frederickson is 25 years old and decides to invest $5000 in a savings account that compounds monthly rate of 14%. After 15 years, how much is in the account?

Answer 1

To calculate the future value of an investment with compound interest, you can use the formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- \(A\) is the amount of money accumulated after time \(t\),
- \(P\) is the principal amount (the initial amount of money),
- \(r\) is the annual interest rate (decimal),
- \(n\) is the number of times that interest is compounded per year,
- \(t\) is the number of years the money is invested for.

In this case:
- \(P = 5000\)
- \(r = 0.14\) (14% as a decimal)
- \(n = 12\) (monthly compounding)
- \(t = 15\)

Now, we can plug these values into the formula:

\[
A = 5000 \left(1 + \frac{0.14}{12}\right)^{12 \times 15}
\]

First, calculate \(\frac{r}{n}\):

\[
\frac{0.14}{12} \approx 0.01166667
\]

Now calculate \(nt\):

\[
nt = 12 \times 15 = 180
\]

Now we can substitute these values into the formula:

\[
A = 5000 \left(1 + 0.01166667\right)^{180}
\]

This simplifies to:

\[
A = 5000 \left(1.01166667\right)^{180}
\]

Now we calculate \((1.01166667)^{180}\):

\[
(1.01166667)^{180} \approx 5.188652236
\]

Now calculate \(A\):

\[
A \approx 5000 \times 5.188652236 \approx 25943.26
\]

So, after 15 years, Carl Frederickson will have approximately **$25,943.26** in the account.