You have just graduated from the MBA program and to reward yourself you have decided to purchase a 2012 BMW 650 sports car. You are scheduled to make a $12,000 down payment on the vehicle and have been told that your monthly payments will be $2,250/month for the next 4 years. The monthly rate charged for the BMW's financing plan is 0.25% (3% APR compounded monthly)

a) How much are you paying for the car?

b) How much is outstanding on the loan at the end of year 3?

c) Why would BMW offer loans at 3% when their cost of borrowing is probably higher than that?

P = Po*(1+r)^n

P = $2250/mo. * 48mo. = $108,000

r = (3%/12)/100% = 0.0025 = Monthly % rate expressed as a decimal.

n = 1comp./mo * 48mo = 48 Compounding periods.

a. P = (Po-12000)*(1.0025)^48 = 108,000
(Po-12000)*1.12733 = 108000
Po-12000 = 95,801.75
Po = $107,801.75 = Initial price.

b. BAL. = 108,000 - 2250*36 = $27,000