Question

Angela deposits $4000 into an account with an APR of 2.4% for 10 years. Find the future value of the account if interest is compounded monthly.

Answer 1

To find the future value of the account with interest compounded monthly, we can use the future value formula for compound interest:

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

where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) 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 or borrowed.

Given:
- \( P = 4000 \)
- \( r = 2.4\% = 0.024 \)
- \( n = 12 \) (monthly compounding)
- \( t = 10 \)

Now, substitute the values into the formula:

\[
A = 4000 \left(1 + \frac{0.024}{12}\right)^{12 \times 10}
\]

Calculating the values inside the parentheses:

\[
\frac{0.024}{12} = 0.002
\]

Now, plug this value back into the formula:

\[
A = 4000 \left(1 + 0.002\right)^{120}
\]
\[
A = 4000 \left(1.002\right)^{120}
\]

Next, calculate \( (1.002)^{120} \):

\[
(1.002)^{120} \approx 1.268241
\]

Now, multiply this value by the principal:

\[
A \approx 4000 \times 1.268241 \approx 5072.96
\]

Therefore, the future value of the account after 10 years is approximately:

\[
\boxed{5072.96}
\]