Question

Sammy borrowed​ $10,000 to purchase a new car at an annual interest rate of​ 11%. She is to pay it back in equal monthly payments over a​ 5-year period. How much total interest will be paid over the period of the​ loan? Round to the nearest dollar.

Answer 1

First we need to find the monthly payments in order to find the interest

Use the formula of the present value of an annuity ordinary which is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 10000
PMT monthly payment?
R interest rate 0.11
K compounded monthly 12 because the payments to repay the loan are monthly
N time 5years
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=10,000÷((1−(1+0.11÷12)^(
−12×5))÷(0.11÷12))
=217.42 per month

After that find total paid amount
5years=60 months
Total paid=217.42×60=13,045.2

Total interest
13,045.2−10,000=3,045.2. Answer