Question

You've just bought a new flat-screen TV for $3,600 and the store you bought it from offers to let you finance the entire purchase at an annual rate of 11 percent compounded monthly. If you take the financing and make monthly payments of $90, how long will it take to pay off the loan? How much will you pay in interest over the life of the loan? I.e. The number of years it will take to pay off the loan is years. (Round to one decimal place.)

Answer 1

It will take approximately 6.9 years to pay off the loan. The total interest paid over the life of the loan is approximately $1,876.80.

Step-by-step explanation:

To calculate the time it will take to pay off the loan, we can use the formula:

Time (in years) = -log((PV - PMT * ((1 + r/12)^(n*12) -1)) / (PMT * r/12)) / (12 * log(1 + r/12))

Where PV is the principal amount, PMT is the monthly payment, r is the annual interest rate (11%), and n is the number of years. Plugging in the values, we get:

Time = -log((3600 - 90 * ((1 + 0.11/12)^(n*12) - 1)) / (90 * 0.11/12)) / (12 * log(1 + 0.11/12))

Solving this equation, we find that it will take approximately 6.9 years to pay off the loan.

To calculate the total interest paid over the life of the loan, we can use the formula:

Total Interest = (PMT * 12 * Time) - PV

Plugging in the values, we get:

Total Interest = (90 * 12 * 6.9) - 3600

Therefore, the total interest paid over the life of the loan is approximately $1,876.80.