
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 4%. How much should you deposit monthly to accumulate $84000 in 12 ​years?

Part 1: You should invest ____ $ each month.

To determine how much you should deposit monthly, we can use the future value of an annuity formula, which is applicable when making regular monthly deposits into an account that earns interest.

The formula is:

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

Where:
- $ FV $ is the future value of the annuity (i.e., $84,000),
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments.

Given:
- APR = 4% annually, so the monthly interest rate $ r = \frac{4\%}{12} = \frac{0.04}{12} = 0.003333 $
- $ n = 12 \times 12 = 144 $ months,
- $ FV = 84,000 $.

Now, we can rearrange the formula to solve for $ P $:

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

Let's calculate this amount.You should invest approximately **$455.44** each month to accumulate $84,000 in 12 years.

Would you like further details or have any questions?

Here are some related questions you might consider:
1. How would the monthly payment change if the APR was 5% instead of 4%?
2. What if you could only invest for 10 years instead of 12 years? How would the payment change?
3. How much total interest would you earn over the 12 years?
4. How would the payment be affected if you made quarterly deposits instead of monthly?
5. What if you wanted to save $100,000 instead of $84,000? What would the monthly payment be?

**Tip:** Small increases in the interest rate can significantly reduce the amount you need to save each month due to the compounding effect over time.

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 4%. How much should you deposit monthly to accumulate $84,000 in 12 years?

Learn how to calculate the monthly deposit required to accumulate $84,000 in 12 years with a 4% APR using the Future Value of an Annuity formula. This detailed explanation covers key financial mathematics concepts suitable for students in Grades 11-12.

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