Question

Your car lease requires a down payment of $1,500 and payments of $450 per month for 36 months. the apr is 6% compounded monthly and payments are made at the end of the month. at the end of the lease, you have the option to buy the vehicle for $20,000 (the residual value). how much is the car worth today? (round to whole number and answer without $ sign)

Answer 1

Monthly interest, i = APR/12 = 0.06/12 = 0.005
Monthly payment, A = $450
Period, n = 36 (months)
Future value of payment
= A((1+i)^n-1)/i
= 450((1.005^36-1)/0.005
= 17701.2472341
Future value of car
F = future value of payment + residual value
= 17701.2472341 + 20000
= 37701.2472341

Present value of car
= downpayment + present value of future payments
= 1500 + F/(1+i)^36
= 1500 + 37701.2472341/(1.005^36)
= 1500 + 31504.86
= 33004.86