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)
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
