Question

Understanding Interest Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Anne invests $7,000 into a retirement account with a compound interest rate of 3.3% compounded quarterly. What is Anne’s final amount after 25 years of investment? Round the answer to the nearest cent.(1 point)
Anne’s final amount after 25 years of investment is $
.
Remaining Attempts : 3

Answer 1

To calculate the final amount of Anne’s investment using the compound interest formula, you can use the following formula:

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

Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = principal amount (the initial amount of money).
- \(r\) = annual interest rate (decimal).
- \(n\) = number of times that interest is compounded per unit \(t\).
- \(t\) = the number of years the money is invested or borrowed.

For Anne's investment:

- \(P = 7000\)
- \(r = 3.3\% = 0.033\)
- \(n = 4\) (since the interest is compounded quarterly)
- \(t = 25\)

Now plug the values into the formula:

\[
A = 7000 \left(1 + \frac{0.033}{4}\right)^{4 \times 25}
\]

Calculating each part step-by-step:

1. Calculate \(\frac{0.033}{4}\):

\[
\frac{0.033}{4} = 0.00825
\]

2. Calculate \(1 + 0.00825\):

\[
1 + 0.00825 = 1.00825
\]

3. Calculate \(4 \times 25 = 100\).

4. Raise \(1.00825\) to the power of 100:

\[
1.00825^{100} \approx 2.246122
\]

5. Finally, multiply by the principal amount:

\[
A \approx 7000 \times 2.246122 \approx 15723.86
\]

Thus, Anne’s final amount after 25 years of investment is approximately **$15,723.86**.

Final answer: Anne's final amount after 25 years of investment is **$15,723.86**.