Question

$25,000 is placed into an account earning an annual interest rate of 3.5%. what is the value if interest is compounded after 7 years

Answer 1

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

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

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.

In your case:
- \(P = 25000\)
- \(r = 0.035\) (3.5% as a decimal)
- \(n = 1\) (assuming interest is compounded annually)
- \(t = 7\)

Now, substituting the values into the formula:

\[
A = 25000 \left(1 + \frac{0.035}{1}\right)^{1 \times 7}
\]

\[
A = 25000 \left(1 + 0.035\right)^{7}
\]

\[
A = 25000 \left(1.035\right)^{7}
\]

Now, calculate \( (1.035)^7 \):

\[
(1.035)^7 \approx 1.269
\]

Now substitute back to find \(A\):

\[
A \approx 25000 \times 1.269 \approx 31672.50
\]

Thus, the value of the account after 7 years is approximately **$31,672.50**.