Derek decides to buy a new car. The dealership offers him achoice of paying $598.00...

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?

Expert Solution

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)

jeff jeffy answered 2 years ago

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