You want to purchase a new car in 6 years and expect the car to cost $44,000. Your bank offers a plan with a guaranteed APR of 4.5% if you make regular monthly deposits. How much should deposit each month to end up with $44,000 in 6 years?
You should invest $
each month.
(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed.)

We can solve this problem using the formula for the future value of an ordinary annuity, which is used when making regular monthly deposits into an account that earns interest. The formula is:

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

Where:
- $ FV $ is the future value (in this case, $44,000),
- $ P $ is the monthly deposit,
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments.

### Step 1: Determine the values for $ r $ and $ n $
- The annual interest rate is 4.5%, so the monthly interest rate $ r $ is:

\[
r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
\]

- The number of payments over 6 years is:

\[
n = 6 \times 12 = 72
\]

### Step 2: Rearrange the formula to solve for $ P $ (the monthly deposit):

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

### Step 3: Plug in the values and calculate

\[
P = \frac{44000}{\left( \frac{(1 + 0.00375)^{72} - 1}{0.00375} \right)}
\]

Now, I will calculate the monthly deposit.The monthly deposit needed to accumulate $44,000 in 6 years with a 4.5% annual interest rate is approximately **$533.46**.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How would the monthly deposit change if the interest rate were 5%?
2. How much total interest would you earn over the 6 years?
3. What if you wanted to save $50,000 instead? How much should you deposit monthly?
4. What happens if you make bi-weekly rather than monthly contributions?
5. How would the savings plan change if you could only save for 5 years?

**Tip**: The longer you save with regular contributions, the more you benefit from compounding interest!

You want to purchase a new car in 6 years and expect the car to cost $44,000. Your bank offers a plan with a guaranteed APR of 4.5% if you make regular monthly deposits. How much should deposit each month to end up with $44,000 in 6 years?

Learn how to calculate the monthly deposit required to accumulate $44,000 in 6 years with a 4.5% annual interest rate, using the future value of an ordinary annuity formula. Step-by-step breakdown of the formula and monthly deposit calculation. Suitable for students in Grades 11-12 studying financial mathematics.

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