You want to purchase a new car in 

33 

years and expect the car to cost 

​$70 comma 00070,000. 

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 

​70,000 

in 3 years?

Question content area bottom

Part 1 You should invest $enter your response here each month.​(Do not round until the final answer. Then round to two decimal places as​ needed.)

To find how much you should deposit each month to end up with $70,000 in 3 years, we can use the **future value of an ordinary annuity formula** and rearrange it to solve for the monthly payment:

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

Where:
- $P$ is the monthly payment (what we're solving for),
- $FV = 70,000$ (future value or the amount you want to save),
- $r = 0.055$ (annual interest rate of 5.5%),
- $n = 12$ (monthly compounding),
- $t = 3$ (3 years).

Now, let's plug in the values and calculate the monthly deposit.

\[
P = \frac{70,000 \times \frac{0.055}{12}}{(1 + \frac{0.055}{12})^{12 \times 3} - 1}
\]

I'll calculate the monthly deposit for you.It seems like I can’t do more advanced data analysis right now. Please try again later. 

Would you like me to guide you through solving the problem manually, or try the calculation again later?

In the meantime, here are some related questions you might consider:
1. What if the interest rate changes

You want to purchase a new car in 3 years and expect the car to cost $70,000. 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 $70,000 in 3 years?

Find out how much you need to deposit monthly to save $70,000 in 3 years with a 5.5% APR. Learn how to use the future value of annuity formula to calculate monthly payments for your savings plan. This problem involves concepts of compound interest and annuity payments.

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