Question

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

Round your answer to the nearest dollar

Answer 1

To calculate the future value of an investment compounded annually, you can use the formula:

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

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).
- \( t \) is the number of years the money is invested or borrowed.

In this case:
- \( P = 4900 \)
- \( r = 8.75\% = 0.0875 \)
- \( t = 12 \)

Now plug the values into the formula:

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

Calculating \( 1 + 0.0875 \):

\[
1 + 0.0875 = 1.0875
\]

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

\[
(1.0875)^{12} \approx 2.2952
\]

Now calculate \( A \):

\[
A \approx 4900 \times 2.2952 \approx 11247.48
\]

Rounding to the nearest dollar, the investment will be worth approximately:

\[
\boxed{11247}
\]

after 12 years.