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This problem is asking you to determine the future value of an Individual Retirement Account (IRA) using an annuity formula and then to calculate the interest earned.

### Given:
- You deposit $10 at the end of each month.
- The interest rate is 4.5% annually, compounded monthly.
- You save from age 24 to 65, which means you are saving for 41 years (or 492 months).

The annuity formula provided is:

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

Where:
- $ A $ is the future value of the annuity (total amount in the account after 41 years).
- $ P $ is the monthly deposit ($10).
- $ r $ is the annual interest rate (4.5% or 0.045).
- $ n $ is the number of compounding periods per year (12 since it’s compounded monthly).
- $ t $ is the number of years (41 years).

Now, let's plug in the values and calculate the future value, $ A $. I'll do that calculation for you.The future value of the IRA after 41 years will be approximately **$14,150.14**.

### Part b: Find the interest.
To calculate the interest earned, subtract the total amount of deposits from the future value:

\[
\text{Interest} = A - \text{Total Deposits}
\]

The total deposits are the monthly deposit multiplied by the number of months you contributed (41 years × 12 months). I'll calculate the interest for you next.The interest earned on the IRA over 41 years will be approximately **$9,230.14**.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does increasing the monthly deposit affect the future value of the IRA?
2. What happens if the interest rate is compounded daily instead of monthly?
3. How would the future value change if the annual interest rate increases to 5%?
4. What is the effect of contributing for only 30 years instead of 41 years?
5. How does a higher interest rate influence the total interest earned?

**Tip:** Always make sure to check whether the interest is compounded annually, monthly, or daily, as it can significantly impact the future value of your investment.

At the age of 24, to save for retirement, you decide to deposit $10 at the end of each month in an IRA that pays 4.5% compounded monthly. Use the given formula to determine how much you will have in the IRA when you retire at age 65. Then, find the interest.

Determine the future value of monthly IRA deposits compounded monthly at a 4.5% interest rate over 41 years. Learn how to use the annuity formula to calculate the total amount and the interest earned, with step-by-step instructions.

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