You want to purchase a new car in 9 years and expect the car to cost ​$10000. Your bank offers a plan with a guaranteed APR of 4.5 % if you make regular monthly deposits. How much should you deposit each month to end up with ​$10000 in 9​ years?

You should invest ​$_____each month.​(Do not round until the final answer. Then round to two decimal places as​ needed.)

This problem involves calculating the regular monthly deposits needed to accumulate a future value using compound interest. The future value (FV) is $10,000, the annual percentage rate (APR) is 4.5%, and the time period is 9 years, with monthly deposits.

We can use the formula for the future value of an annuity:

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

Where:
- $FV$ is the future value, which is $10,000.
- $P$ is the monthly deposit amount (the unknown we need to find).
- $r$ is the annual interest rate (4.5% or 0.045).
- $n$ is the number of times the interest is compounded per year (12 for monthly deposits).
- $t$ is the number of years (9 years).

Rearranging the formula to solve for $P$:

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

Now we can plug in the known values and calculate $P$.You should invest approximately **$75.28** each month to end up with $10,000 in 9 years.

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How does changing the APR affect your monthly deposit?
2. What if the time period was 12 years instead of 9 years?
3. How would annual deposits instead of monthly deposits affect the calculation?
4. What is the total amount you deposited over 9 years?
5. What if the future value target was $15,000 instead of $10,000?

**Tip:** To minimize your monthly payments, consider increasing the investment period or finding a higher interest rate plan.

You want to purchase a new car in 9 years and expect the car to cost ​$10,000. Your bank offers a plan with a guaranteed APR of 4.5% if you make regular monthly deposits. How much should you deposit each month to end up with ​$10,000 in 9​ years? You should invest ​$_____ each month.​ (Do not round until the final answer. Then round to two decimal places as​ needed.)

Learn how to calculate the monthly deposits required to save $10,000 for a new car in 9 years using a guaranteed 4.5% APR. This problem involves the future value of annuity formula and compound interest calculations. Suitable for Grades 10-12 students.

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