Question

A principal of $4800 is invested at 5% interest, compounded annually. How much will the investment be worth after 12 years?
Use the calculator provided and round your answer to the nearest dollar.

Answer 1

To calculate the future value of an investment with compound interest, 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.

Given:
- \( P = 4800 \)
- \( r = 5\% = 0.05 \)
- \( t = 12 \)

Now, plug in the values:

\[
A = 4800(1 + 0.05)^{12}
\]
\[
A = 4800(1.05)^{12}
\]

Now, calculate \( (1.05)^{12} \):

\[
(1.05)^{12} \approx 1.795856326
\]

Now, multiply this by the principal:

\[
A \approx 4800 \times 1.795856326 \approx 8619.99999
\]

Rounding to the nearest dollar, the investment will be worth approximately **$8620** after 12 years.