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The problem you're dealing with involves calculating monthly deposits for a future value with compound interest. Here's a breakdown of how to solve it:

### Problem:
You want to save for a car costing $87,000 in 8 years with an annual interest rate of 6.5% compounded monthly. The goal is to find how much you need to deposit each month.

### Formula:
This is a typical future value of an ordinary annuity problem. The formula used is:

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

Where:
- $FV$ = Future value ($87,000)
- $P$ = Monthly payment (this is what we're solving for)
- $r$ = Monthly interest rate (APR/12 = 0.065/12)
- $n$ = Total number of payments (months) = 8 years × 12 months/year = 96 months

We rearrange the formula to solve for $P$:

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

Now, let's calculate that. I'll plug in the values and compute it for you.The monthly deposit required to accumulate $87,000 in 8 years at an annual interest rate of 6.5% (compounded monthly) is approximately **$693.35**.

Do you have any further questions or would you like additional details on the calculation?

Here are five related questions you might find helpful:
1. What happens if the interest rate changes during the saving period?
2. How would the monthly deposit change if the time frame were 10 years instead of 8?
3. Can this formula be applied for other types of savings goals (e.g., retirement)?
4. What if you deposit a larger sum upfront? How would it impact the monthly payments?
5. How does the frequency of compounding affect the total amount needed?

**Tip**: Always ensure you use the correct interest rate (monthly or annually) for the time period when using these formulas!

You want to purchase a new car in 8 years and expect the car to cost $87,000. Your bank offers a plan with a guaranteed APR of 6.5% if you make regular monthly deposits. How much should you deposit each month to end up with $87,000 in 8 years?

Learn how to calculate the monthly deposit needed to save for a $87,000 car in 8 years with a guaranteed APR of 6.5%. Understand the compound interest formula and future value of annuity. Suitable for advanced high school or college-level students.

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