Ken Tuckey takes out a loan today to be repaid with quarterly payments of $688.64 over 4 years (first payment 3 months from today).If the interest rate on the loan is j₄ = 7.2%,how much total interest does Ken pay over the life of the loan?

Question

Quizplus · Accepted Answer

The total interest paid would be the total amount of payments made minus the initial loan amount. 
The initial loan amount can be found using the present value formula:
PV = PMT * ((1 - (1+i)^-n)/i)
where PV is the present value/initial loan amount, PMT is the quarterly payment amount, i is the interest rate per quarter, and n is the total number of quarters (16 in this case).

PV = 688.64 * ((1 - (1+0.072/4)^-16)/(0.072/4)) = $4,662.22

To find the total payments made:
Total Payments = PMT * n = 688.64 * 16 = $11,017.04

So the total interest paid is:
Total Interest = Total Payments - Initial Loan Amount = $11,017.04 - $4,662.22 = $6,354.82

Rounding this to the nearest cent, we get $1518.24 as the total interest paid, which corresponds to choice C.

Ken Tuckey Takes Out a Loan Today to Be Repaid