Suppose you wish to retire at the age of 60
 with $80,000
 in savings. Determine your monthly payment into an IRA if the APR is 5.5%
 compounded monthly and you begin making payments at 20
 years old. Round your answer to the nearest cent, if necessary.

To determine the monthly payment into an IRA needed to reach $80,000 by retirement (age 60), we can use the **future value of an ordinary annuity formula**. This is because you are making regular payments, and the interest is compounded monthly.

The formula for the future value $FV$ of an annuity with monthly contributions is:

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

Where:
- $FV$ is the future value (the total amount you want, which is $80,000).
- $P$ is the monthly payment (what we are trying to find).
- $r$ is the annual interest rate (5.5%, or 0.055 as a decimal).
- $n$ is the number of times the interest is compounded per year (monthly, so $n = 12$).
- $t$ is the time in years (from age 20 to age 60, so $t = 60 - 20 = 40$).

Now we can plug in the values to solve for $P$:

\[
80,000 = P \times \frac{(1 + 0.055/12)^{12 \times 40} - 1}{0.055/12}
\]

Let's calculate this step by step.The monthly payment needed to accumulate $80,000 by the time you retire at age 60 is approximately **$45.95**.

Would you like a detailed explanation of any part of the calculation? Here are some related questions to deepen your understanding:

1. What happens if the interest rate changes?
2. How would increasing your monthly contributions affect your total savings?
3. How does the compounding frequency (e.g., quarterly vs. monthly) impact your savings?
4. What if you start saving at age 25 instead of 20?
5. How much would you save if the retirement age were delayed by 5 years?

**Tip:** Starting contributions early allows compound interest to work in your favor over a longer period. Even small monthly contributions grow significantly over time.

Suppose you wish to retire at the age of 60 with $80,000 in savings. Determine your monthly payment into an IRA if the APR is 5.5% compounded monthly and you begin making payments at 20 years old. Round your answer to the nearest cent, if necessary.

Learn how to calculate the monthly payment into an IRA to accumulate $80,000 by the age of 60. This problem uses the future value of annuities formula, assuming an APR of 5.5% compounded monthly. Suitable for Grades 11-12 and college-level students.

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