At age 38​, you start saving for retirement. If your investment plan pays an APR of 7​% and you want to have ​$1.2 million when you retire in 27 ​years, how much should you deposit​ monthly?

To solve this, we can use the **future value of an annuity formula**, as you are making regular monthly deposits and earning interest. The formula is:

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

Where:
- $ FV $ is the future value (the amount you want to have), which is $1.2 million.
- $ P $ is the monthly deposit (what we want to find).
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the number of months (number of years multiplied by 12).

### Step 1: Define the values
- $ FV = 1,200,000 $
- $ APR = 7\% $ or 0.07 annually, so $ r = \frac{0.07}{12} \approx 0.005833 $
- $ n = 27 \times 12 = 324 $ months

### Step 2: Rearrange the formula to solve for $ P $
\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

Now, I'll calculate this.To reach your goal of $1.2 million in 27 years with an APR of 7%, you should deposit approximately **$1,253.78** every month.

Would you like further details or have any questions about this? Here are some related questions to consider:

1. How does the monthly deposit change if the APR is 6% instead of 7%?
2. What if you want to retire in 20 years instead of 27 years? How much would you need to deposit monthly?
3. How does compound interest affect the final amount in this investment?
4. What happens if you make a one-time lump sum deposit instead of monthly contributions?
5. How does inflation impact the purchasing power of $1.2 million over 27 years?

**Tip:** Starting early with even small contributions can lead to significant growth due to the power of compound interest.

At age 38, you start saving for retirement. If your investment plan pays an APR of 7% and you want to have $1.2 million when you retire in 27 years, how much should you deposit monthly?

Discover how to calculate the monthly deposit needed to reach $1.2 million for retirement in 27 years with an APR of 7%. This financial mathematics problem involves understanding compound interest and annuities, suitable for Grades 11-12 and college students.

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