Question

You want to purchase a new car in 6 years and expect the car to cost $12,000. 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 $12,000 in 6 years?
T
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

Answer 1

To calculate the monthly deposit required, we can use the formula for future value of an annuity, which is:

FV = Pmt x (((1 + r)^n - 1) / r)

where FV is the future value, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case, we want to find the monthly payment required to achieve a future value of $12,000 in 6 years, or 72 months. The monthly interest rate is the annual percentage rate (APR) divided by 12, so:

r = 6.5% / 12 = 0.00541666667

Substituting these values into the formula, we get:

12,000 = Pmt x (((1 + 0.00541666667)^72 - 1) / 0.00541666667)

Solving for Pmt, we get:

Pmt = 12,000 / (((1 + 0.00541666667)^72 - 1) / 0.00541666667)

≈ $164.41

Therefore, you should deposit $164.41 each month to end up with $12,000 in 6 years