The Problem:

Holly wants to explore the difference between buying and leasing a vehicle, both over 5 years with monthly payments. The car that she has an interest in has a value of $27000, and is located in Winkler, MB. If she purchases the vehicle, she can do so with 3% financing. If she leases the vehicle, there is a residual rate of 51%, an acquisition fee of $495 and an interest rate of 5% (no security deposit is required).

Find the monthly payments for the purchase and lease of the vehicle. Holly wishes to lease the vehicle and invest what she saves on every month's payment in a savings account with an interest rate of 6.4%, compounded monthly.

After the 5 years, she wishes to take the value of her investment and use it to buy out the residual value of the car. When she does that, how much is she left with/does she owe?