Suppose you wish to retire at the age of 7070 with $80,000$80,000 in savings. Determine your monthly payment into an IRA if the APR is 5.5%5.5% compounded monthly and you begin making payments at 2525 years old. Round your answer to the nearest cent, if necessary.
 

Formulas

**Present Value with Compound Interest**

PV=A(1+rn)ntPV=A(1+rn)nt

**Annuity Payment Amount**

PMT=FV⋅(rn)[(1+rn)nt−1]PMT=FV⋅(rn)[(1+rn)nt−1]

**Future Value of an Annuity**

FV=PMT⋅[(1+rn)nt−1](rn)FV=PMT⋅[(1+rn)nt−1](rn)

To determine the monthly payment into the IRA, we will use the **Annuity Payment Amount** formula:

\[
\text{PMT} = \frac{FV \cdot \left(\frac{r}{n}\right)}{\left(1 + \frac{r}{n}\right)^{nt} - 1}
\]

Where:
- $ \text{PMT} $ is the monthly payment.
- $ FV $ is the future value, which is $80,000.
- $ r $ is the annual interest rate, which is 5.5% or 0.055.
- $ n $ is the number of compounding periods per year, which is 12 (monthly compounding).
- $ t $ is the number of years between the start (age 25) and retirement (age 70), so $ t = 70 - 25 = 45 $.

Now, let's plug in the values:

\[
\text{PMT} = \frac{80,000 \cdot \left(\frac{0.055}{12}\right)}{\left(1 + \frac{0.055}{12}\right)^{12 \times 45} - 1}
\]

I will calculate this for you now.The monthly payment you would need to make into the IRA is approximately **$33.90**.

Would you like more details or explanations? Here are 5 related questions to explore further:

1. How does changing the interest rate affect your monthly payment?
2. What if you wanted to retire earlier, say at age 60? How would that change the payment?
3. How would different compounding periods (e.g., quarterly) affect your savings?
4. What would be the impact of increasing your retirement savings goal to $100,000?
5. How does inflation affect the value of your retirement savings?

**Tip:** Starting early with smaller payments is more beneficial due to the compounding effect over time!

Suppose you wish to retire at the age of 70 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 25 years old. Round your answer to the nearest cent, if necessary.

Learn how to calculate the monthly payment into an IRA needed to retire with $80,000 in savings by age 70. This problem involves using the annuity payment formula with a 5.5% APR compounded monthly, starting at age 25. Perfect for students studying compound interest, annuities, and future value calculations.

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