You are to make monthly deposits of $450 into a retirement account that pays an APR of 10.7 percent compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 32 years?

To calculate the future value of the retirement account, we can use the formula for the future value of an annuity (regular monthly payments):

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

Where:
- $FV$ is the future value of the account.
- $P$ is the monthly deposit amount.
- $r$ is the monthly interest rate (APR divided by 12 months).
- $n$ is the total number of deposits (number of months).
  
Given:
- $P = 450$ dollars,
- APR = 10.7% (or 0.107 as a decimal),
- Monthly interest rate $r = \frac{0.107}{12}$,
- Time $t = 32$ years, so the total number of deposits $n = 32 \times 12 = 384$ months.

Let me now calculate the future value of the retirement account.The future value of your retirement account after 32 years, with monthly deposits of $450 and an APR of 10.7% compounded monthly, will be approximately **$1,475,143.62**.

Would you like any additional details or clarifications?

Here are 5 related questions you might be interested in:
1. How would the future value change if the APR were lower or higher?
2. What would happen if the deposits were made at the beginning of each month instead of at the end?
3. How does the formula for an annuity differ from other types of interest calculations?
4. What if you started with an initial lump sum in the account as well as the monthly deposits?
5. How much would you have if you made deposits for a shorter period, like 20 years instead of 32?

**Tip:** Increasing your monthly deposit amount even slightly can significantly increase your retirement fund due to the power of compound interest.

Learn how to calculate the future value of a retirement account with $450 monthly deposits, 10.7% APR compounded monthly, over 32 years. This problem covers key concepts in compound interest and annuities, using the future value formula. Suitable for students in Grades 10-12.

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