Suppose you wish to retire at the age of 60 with $70,000 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 sent if necessary

To determine your monthly payment into an IRA (Individual Retirement Account) in order to retire at age 60 with $70,000 in savings, we can use the **future value of an annuity formula**. This formula is used to calculate regular payments that will grow to a certain amount over time, given a certain interest rate compounded periodically.

The formula for the future value of an annuity is:

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

Where:
- $ FV $ is the future value ($70,000),
- $ P $ is the monthly payment (the amount we need to find),
- $ r $ is the monthly interest rate (APR divided by 12),
- $ n $ is the total number of payments (number of months between 25 and 60 years old).

### Step-by-step Calculation:

1. **Interest Rate (r)**:  
   The annual percentage rate (APR) is 5.5%, so the monthly interest rate is:
   \[
   r = \frac{5.5\%}{12} = \frac{0.055}{12} = 0.0045833
   \]

2. **Number of Payments (n)**:  
   You will be contributing for 35 years (from age 25 to age 60), so the total number of payments is:
   \[
   n = 35 \times 12 = 420 \text{ months}
   \]

3. **Future Value (FV)**:  
   The desired future value of the IRA is $70,000.

Now, we can rearrange the formula to solve for $ P $ (the monthly payment):

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

Let's plug in the values:

\[
P = \frac{70,000 \times 0.0045833}{(1 + 0.0045833)^{420} - 1}
\]

I will calculate this now.The monthly payment required to accumulate $70,000 in savings by the time you retire at age 60, with an APR of 5.5% compounded monthly, is approximately **$55.08**.

Do you have any questions or need further details?

Here are five related questions to explore this further:
1. What happens if the interest rate changes?
2. How would increasing the monthly contribution affect the future value?
3. What is the impact of starting contributions at an earlier or later age?
4. How does the compounding frequency (e.g., quarterly or daily) affect the savings growth?
5. What if you wanted to retire with a different amount, say $100,000 or $200,000?

**Tip**: Starting to invest early in an IRA allows more time for compound interest to work in your favor, reducing the amount you need to contribute monthly.

Suppose you wish to retire at the age of 60 with $70,000 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 monthly payments into an IRA to reach $70,000 in savings by age 60 with a 5.5% APR compounded monthly. This example uses the future value of an annuity formula and involves making contributions from age 25 to 60. Ideal for students and individuals planning for retirement.

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