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The problem in the image involves calculating the monthly deposit Celine needs to make to reach her goal of $1,200,000 by age 67, assuming an APR of 7% compounded monthly.

This is a future value of an annuity problem. The formula we use is:

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

Where:
- $ FV $ is the future value ($1,200,000),
- $ P $ is the monthly payment (the value we are solving for),
- $ r $ is the annual interest rate (7% or 0.07),
- $ n $ is the number of times the interest is compounded per year (12 for monthly),
- $ t $ is the number of years Celine will be contributing (from age 22 to 67, so 45 years).

Let’s substitute the known values into the formula and solve for $ P $. 

\[
1,200,000 = P \times \frac{(1 + 0.07/12)^{12 \times 45} - 1}{0.07/12}
\]

Now, I'll calculate the value of $ P $.The monthly deposit Celine needs to make in order to reach her goal of $1,200,000 by age 67 is approximately **$316.41**.

Would you like further details or clarifications?

Here are five related questions to expand on this topic:
1. How does the monthly deposit change if the APR increases to 8%?
2. What would happen if Celine started depositing at age 30 instead of 22?
3. How does changing the compounding frequency (e.g., from monthly to quarterly) affect the monthly deposit?
4. What is the effect of reducing the future value target to $1,000,000?
5. How long would it take Celine to reach $1,200,000 if she deposits $500 monthly?

**Tip**: Compound interest grows faster the more frequently it's compounded, so even small monthly contributions can add up significantly over time.

Celine wishes to retire at age 67 with $1,200,000 in her retirement account. When she turns 22, she decides to begin depositing money into an account with an APR of 7% compounded monthly. What is the monthly deposit that Celine must make in order to reach her goal?

Calculate the monthly deposit needed for Celine to retire with $1,200,000, starting at age 22 with a 7% APR compounded monthly. This problem covers future value of annuity concepts and compound interest calculations.

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