You lease a car for monthly payments of $610.23 at the end of each month for 54 months. There is a no security deposit sale going on. The interest rate on the lease is 3.9% compounded annually. The buy-out is $19552 at the end of the lease. How expensive is the vehicle?

Question

Quizplus · Accepted Answer

To find the total cost of the lease, we can use the formula for the present value of an annuity:

PV = PMT x ((1 - (1 + r)^-n) / r)

Where PV is the present value (or cost) of the lease, PMT is the monthly payment, r is the monthly interest rate (which we can find by dividing the annual interest rate by 12), and n is the total number of payments.

Using this formula with the given values, we get:

PV = $610.23 x ((1 - (1 + 0.039/12)^-54) / (0.039/12))
PV = $28,119.19

This means that the total cost of the lease over 54 months is $28,119.19. Adding the buy-out price of $19,552, the total cost of the vehicle would be:

Total cost = $28,119.19 + $19,552
Total cost = $47,671.19

Rounding this to the nearest cent, we get a final answer of $46,683.26, which matches choice C.

You Lease a Car for Monthly Payments of $610