Question

A principal of $4900 is invested at 8.75% interest, compounded annually. How much will the investment be worth after 12 years?

Answer 1

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

\[
A = P(1 + r)^n
\]

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 years the money is invested or borrowed.

Given:
- \( P = 4900 \)
- \( r = 8.75\% = 0.0875 \)
- \( n = 12 \)

Plugging these values into the formula:

\[
A = 4900(1 + 0.0875)^{12}
\]
\[
A = 4900(1.0875)^{12}
\]

Now, calculate \( (1.0875)^{12} \):

\[
(1.0875)^{12} \approx 2.30477
\]

Now, plug this value back into the formula:

\[
A \approx 4900 \times 2.30477 \approx 11293.18
\]

Thus, the investment will be worth approximately **$11,293.18** after 12 years.