Question

You've just bought a new​ flat-screen TV for ​$4,000 and the store you bought it from offers to let you finance the entire purchase at an annual rate of 13

percent compounded monthly. If you take the financing and make monthly payments of ​$150, how long will it take to pay off the​ loan? How much will you pay in interest over the life of the​ loan?

A. The number of loan years is:

B. How much will you pay in interest over the life of the​ loan?

Answer 1

Price of TV = $4000

So, loan amount PV = $4000

interest rate charged r = 13% compounded monthly,

monthly payment PMT = $150

So, number of months N require to repay the loan is calculated using formula:

PV = PMT*(1 - (1+r/n)^(-N))/(r/n)

So, 4000 = 150*(1 - (1+0.13/12)^(-N))/(0.13/12)

Solving this, we get N = 31.64 months

So, The number of loan years is 31.64/12 = 2.64 years

So total payment made over the life of loan = number of month*monthly payments = 31.64*150 = $4746.05

So, Interest payment over the life of loan = total payment - loan amount = 4746.05 - 4000 = $746.05