Question

Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?

Answer 1

The formula for the present value of an annuity is given by PV = (1 - (1 + r/t)^-nt) / (r/t), so plugging in our values above
28798 = 525(1 - (1 + r/12)^-(5 x 12)) / (r/12)

8798r / 12 = 525(1 - (1 + r/12)^-60)

28798r / (12 x 525) = 1 - (1 + r/12)^-60 2057r / 450 = 1 - (1 + r/12)^-60
So by trial error, let us use r = 37% = 0.37

2057r / 450 = 2057(0.37) / 450

= 761.09 / 450

= 1.691 1 - (1 + r/12)^60

= 1 - (1 + 0.37/12)^-60

= 1 - 0.1617 = 0.8383


Therefore, r is not 37%

Trying r = 3.7% = 0.037

2057r / 450 = 2057(0.037) / 450= 76.109 / 450

= 0.1691 1 - (1 + r/12)^60

= 1 - (1 + 0.037/12)^-60

= 1 - 0.8313

= 0.1687
Therefore, r is approximately 3.7%