You want to purchase a new car in 3 years and expect the car to cost $30,000. Your bank offers a plan with a guaranteed APR of 5.5% if you make regular monthly deposits. How much should you deposit each month to end up with $30,000 in 3 years?

This problem involves calculating the regular monthly deposits needed to accumulate a future value (FV) of $30,000 over a period of 3 years, given an annual interest rate of 5.5% compounded monthly.

We can use the **future value of a series of regular deposits formula**, which is:

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

Where:
- $FV = 30,000$ (the future value you want to have)
- $P$ = the monthly deposit (this is what we're solving for)
- $r = \frac{APR}{12} = \frac{0.055}{12} = 0.0045833$ (the monthly interest rate)
- $n = 3 \times 12 = 36$ (the total number of months over 3 years)

Rearranging the formula to solve for $P$:

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

Now, substitute the values:

\[
P = \frac{30,000 \times 0.0045833}{(1 + 0.0045833)^{36} - 1}
\]

Let me calculate this for you.The monthly deposit you need to make is approximately **$768.38** to accumulate $30,000 in 3 years, given a 5.5% annual interest rate compounded monthly.

Would you like further details on this, or do you have any questions?

Here are five related questions to explore:
1. How would the monthly deposit change if the APR were 6%?
2. What if you could extend the savings period to 5 years—how would the monthly deposit be affected?
3. How much interest will you have earned after 3 years?
4. How does the compounding frequency (e.g., quarterly vs. monthly) affect the required deposits?
5. What if the goal amount were $40,000 instead of $30,000?

**Tip:** Making deposits earlier and more frequently generally reduces the total amount you need to save monthly due to compound interest working over a longer period.

Learn how to calculate the monthly deposits required to save $30,000 in 3 years using a 5.5% APR compounded monthly. This guide covers key financial concepts such as compound interest and future value calculations, suitable for high school students in Grades 10-12.

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