Suppose you wish to retire at the age of 70
with $90,000
in savings. Determine your monthly payment into an IRA if the APR is 7.5%
compounded monthly and you begin making payments at 35
years old. Round your answer to the nearest cent, if necessary.

To determine the monthly payment needed to reach $90,000 by the age of 70, given a 7.5% APR compounded monthly, we will use the **future value of an annuity formula**:

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

Where:
- $FV$ = Future value, which is $90,000.
- $P$ = Monthly payment (what we need to find).
- $r$ = Annual interest rate (7.5% or 0.075).
- $n$ = Number of compounding periods per year (monthly compounding, so $n = 12$).
- $t$ = Number of years (from age 35 to 70, so $t = 70 - 35 = 35$).

Now, let's solve for $P$ (the monthly payment). First, rearrange the formula to isolate $P$:

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

Let me calculate this for you.The monthly payment you need to make into the IRA to reach $90,000 by age 70, with a 7.5% APR compounded monthly, is **$44.32**.

Would you like further details on the calculation, or do you have any other questions?

Here are 5 related questions to consider:
1. How would the monthly payment change if the interest rate were higher?
2. What would be the final savings if you only saved for 30 years?
3. How would switching to quarterly compounding affect the payment?
4. How much would you save with an APR of 6% instead of 7.5%?
5. What happens if you start saving at age 40 instead of 35?

**Tip:** Starting earlier reduces the monthly contribution needed for the same retirement goal due to the power of compound interest!

Suppose you wish to retire at the age of 70 with $90,000 in savings. Determine your monthly payment into an IRA if the APR is 7.5% compounded monthly and you begin making payments at 35 years old. Round your answer to the nearest cent, if necessary.

Discover how to calculate the monthly payment into an IRA to reach $90,000 in savings by age 70, starting at age 35, with an APR of 7.5% compounded monthly. Learn the future value of annuities formula, key compound interest concepts, and step-by-step solutions. Suitable for high school students or anyone planning for retirement.

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