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:
3.7%
Step-by-step explanation:
Given:
Cost = $32,998
Down payment = $4,200
Remaining amount = $32,998 - $4,200 = $28,798
Monthly payment = $525
Duration = 5 years
Present value = Monthly payment × \([\frac{(1-(1+\frac{r}{k})^{-kn})}{(\frac{r}{k})}]\)
here, k = 12 when compounded monthly
r is the rate of interest
thus,
$28,798 = $525 × \([\frac{(1-(1+\frac{r}{12})^{-12\times5})}{(\frac{r}{12})}]\)
or
54.85 = \([\frac{(1-(1+\frac{r}{12})^{-12\times5})}{(\frac{r}{12})}]\)
or
r = 3.7%