Suppose that you borrow ​$15 comma 000 for five years at 6​% toward the purchase of a car. Use PMT equals (P ((r)/(n)))/(1 - (1 + (r)/(n))^-) to find the monthly payments and th…

Question

Suppose that you borrow ​$15 comma 000 for five years at 6​% toward the purchase of a car. Use PMT equals
`(P ((r)/(n)))/(1 - (1 + (r)/(n))^-)` to find the monthly payments and the total interest for the loan.

Answer 1

Monthly payments = $ 289.992

Total interest = $ 2399.520

Explanation:

Given formula of monthly payments,

`PMT=(P((r)/(n)))/(1-(1+(r)/(n))^(-nt))`

Where,

P = present value,

r = annual interest rate,

n = number of months in a year ( i.e. 12 months ),

t = number of years,

Here,

P = $ 15,000,

t = 5 years,

r = 6% = 0.06

Hence, the monthly payment would be,

`PMT=(15000((0.06)/(12)))/(1-((0.06)/(12))^(-60))`

`=(15000(0.005))/(1-(0.005)^(-60))`

`\approx \$ 289.992`

Also, the total interest of the loan = monthly payment × number of months - present value of loan

= 289.992 × 60 - 15000

= $ 2399.520