You deposit $4,500 each year into an account earning 7.5% interest compounded annually.

How much will you have in the account in 19 years?

Do not round numbers while working on the problem. Only round the final answer.

Since we are working with money, round to the cent.

To calculate the future value of an annuity where regular payments are made into an account that earns compound interest, we use the **Future Value of an Annuity formula**:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ P $ is the annual payment ($4,500).
- $ r $ is the annual interest rate (7.5% or 0.075).
- $ n $ is the number of periods (19 years).

Let's plug in the values:

\[
FV = 4500 \times \frac{(1 + 0.075)^{19} - 1}{0.075}
\]

First, calculate $ (1 + 0.075)^{19} $:

\[
(1.075)^{19} \approx 3.815619092
\]

Now, subtract 1 from this value:

\[
3.815619092 - 1 = 2.815619092
\]

Next, divide this result by the interest rate $ r = 0.075 $:

\[
\frac{2.815619092}{0.075} \approx 37.54158857
\]

Finally, multiply this by the annual payment $ P = 4500 $:

\[
4500 \times 37.54158857 \approx 168,937.1496
\]

So, the future value of the account after 19 years, rounded to the nearest cent, is **$168,937.15**.

Would you like more details or have any questions?

Here are some related questions:
1. How would the future value change if the interest rate were higher?
2. What would be the future value if the deposits were made monthly instead of annually?
3. How much interest would be earned in total after 19 years?
4. What if you deposited $4,500 every six months instead?
5. How would inflation affect the purchasing power of this amount?

**Tip:** Regularly review your financial goals to adjust contributions and take advantage of compounding interest.

Learn how to calculate the future value of an annuity with compound interest. This problem involves regular payments, compound interest at 7.5% annually, and spans 19 years. Follow the step-by-step solution using the Future Value of an Annuity formula.

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