Question

Derek decides to buy a new car. The dealership offers him a choice of paying $598.00 per month for 5 years (with the first payment due next month) or paying some amount today. He can borrow money from his bank to buy the car. The bank requires a 6.00% interest rate. What is the most that he would be willing to pay today rather than making the payments?

Answer 1

Solution

The maximum amount he will be willing to pay today is equal to the presenent value of annuity payments he could make to dealer

Present value of annuity =Annuity payment*((1-(1/(1+r)^n))/r)

where

r-discount rate per period-6/12=.5% per month

n-number of periods -12*5=60

Annuity payment-598

Putting values in formula

Present value of annuity =598*((1-(1/(1+.005)^60))/.005)

Solving we get Present value of annuity =$30931.89 (Most he would be willing to pay today)