Question

You want to buy a car. The car costs $101,500. The Tesla dealer offers to finance your car with a 60 month loan at an APR of 12.75%, compounded monthly. Your first payment will be due tomorrow. If you take this loan, what will your monthly car payment be?

Answer 1

Monthly payment for loan of immediate installment can be computed using formula for PV of annuity due as:

PV = P + P x {1-(1+r)^-(n-1)/r}

PV = P [1 + {1-(1+r)^-(n-1)/r}

PV = Present value of annuity = $ 101,500

P = Periodic payment

r = rate per period = 12.75 % p.a. or 0.1275/12 = 0.010625 p.m.

n = No. of periods = 60

$ 101,500 = P [1 + {1-(1+0.010625)^-(60-1)/ 0.010625}]

$ 101,500 = P [1 + {1-(1.010625)^-59/ 0.010625}]

$ 101,500 = P [1 + {(1-0.536028402485)/ 0.010625}]

$ 101,500 = P [1 + (0.463971597515/ 0.010625)]

$ 101,500 = P (1 + 43.667915060256)

$ 101,500 = P x 44.667915060256

P = $ 101,500 / 44.667915060256

P = $ 2,272.32455025221 or $ 2,272.32

Monthly payment will be $ 2,272.32