Question

You buy a car for $30,000 and are going to finance it over 6 years. The dealership make you two offers. You can either have 0% interest for the first 3 years and a nominal annual rate of 6% compounded monthly for the last 3 years or you can have a nominal annual rate of 3% compounded monthly for all 6 years. In either case you are expected to make monthly payments at the end of each month for the 6 years. Which deal should you take? Please justify your answer with computations.

Answer 1

In option 1:

interest rate (i) = 6%/12 = 0.5% or 0.005

Time period (n) = 3 years or 36 months

PV = 30,000

PV formula for annuity is:

PV = A*{ 1 - (1+i)^(-n) }/i

wher A is the monthly payment done

=> 30000 = A {1-(1+0.005)^(-36)}/0.005

=> A = 912.66

Total amount repaid = 912.66*36 = 32,855.69

In option 2

interest rate = 3%/12 = 0.25% or 0.0025

Time period = 6 years or 72 months

PV = A*{ 1 - (1+i)^(-n) }/i

=> 30000 = A {1-(1+0.0025)^(-72)}/0.0025

=> A = 455.81

Total amount repaid = 455.81*72 = 32,818.34

So option 2 is cheaper than option 1 as we are repaying less here. So option 2 shpu;d be selected.