Question

Suppose that you borrow ​$13,000 for three years at 5​% toward the purchase of a car. Use $PMT = \frac{P\frac{r}{n}}{1-(1+\frac{r}{n})^-}$ to find the monthly payments and the total interest for the loan.

Answer 1

Answer:

PMT is 389.62

Total interest for the loan is $ 1026.32

Step-by-step explanation:

Given formula of monthly payment,

$PMT=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}$

Where,

P = Present value of the loan,

r = annual rate of interest,

n = number of months in a year,

t = number of years,

Here, P = $13,000, n = 12 months, r = 5% = 0.05, and t = 3 years,

Hence, the monthly payment,

$PMT=\frac{13000\times \frac{0.05}{12}}{1-(1+\frac{0.05}{12})^{-36}}$

≈ 389.62,

Therefore,

The amount of total interest paid = PMT × nt - P

= 389.62 × 36 - 13000

= 14026.32 - 13000

= $ 1026.32