How much would you need to deposit in an account each month in order to have $40,000 in the account in 9 years? Assume the account earns 5% interest.

To determine how much you need to deposit each month to accumulate $40,000 in an account with a 5% annual interest rate over 9 years, we can use the future value of an ordinary annuity formula:

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

Where:
- $ FV $ is the future value of the annuity ($40,000),
- $ P $ is the monthly deposit,
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of deposits (months).

### Given:
- $ FV = 40,000 $
- Annual interest rate = 5% → Monthly interest rate $ r = \frac{0.05}{12} = \frac{0.05}{12} \approx 0.0041667 $
- Total months $ n = 9 \times 12 = 108 $

### Rearranging the formula to solve for $ P $:

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

### Plugging in the values:

\[
P = \frac{40,000 \times 0.0041667}{(1 + 0.0041667)^{108} - 1}
\]

Calculating:

1. Calculate $ (1 + 0.0041667)^{108} $:
   - $ (1.0041667)^{108} \approx 1.491825 $

2. Now substitute back into the formula:

\[
P = \frac{40,000 \times 0.0041667}{1.491825 - 1} = \frac{166.668}{0.491825} \approx 338.42
\]

### Conclusion:
You would need to deposit approximately **$338.42** each month to have $40,000 in the account after 9 years at a 5% interest rate.

If you want more details or have questions, feel free to ask! Here are some related questions to consider:

1. What if the interest rate was higher or lower? 
2. How would the total amount change if you deposited more or less each month?
3. What are the effects of compounding frequency on the final amount?
4. How does inflation impact the future value of your savings?
5. What are other investment options that might yield higher returns? 

**Tip:** Consider using a financial calculator or software to easily adjust variables like interest rates and time periods for your savings plans.

Discover how to calculate the monthly deposit required to reach $40,000 in 9 years with a 5% interest rate. This detailed guide covers the future value of annuity formula and provides insights into financial planning for students in Grades 10-12.

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