Final answer:
By using the loan payment formula, Harold's monthly payment comes out to be $162.57. Over five years, he pays a total of $9,754.20, resulting in a finance charge of $1,754.20, making option c the correct answer.
Step-by-step explanation:
To determine Harold's monthly payment for a $8,000 loan at an APR (Annual Percentage Rate) of 6.75% over five years, we will use the formula for an installment loan payment which can be found in a mathematics class or financial textbook. This is a typical problem in high school or college business math courses. We use the formula for the monthly payment P on a loan amount A with an interest rate r for n months, which is usually expressed as:
P = A * [r(1+r)^n] / [(1+r)^n - 1]
First, we have to convert the annual interest rate to a monthly rate by dividing by 12, and the loan term from years to months:
- Monthly interest rate: 6.75% / 12 = 0.5625%
- Total number of payments (n): 5 years * 12 months/year = 60
The monthly interest rate in decimal form is 0.5625 / 100 = 0.005625. Now we can plug the values into the formula to find the monthly payment, P:
P = $8,000 * [0.005625(1+0.005625)^60] / [(1+0.005625)^60 - 1]
Calculating P gives us the monthly payment. Once we have P, we can multiply by 60 to get the total amount paid over the loan, and subtract the original $8,000 to find the finance charge. Based on these calculations, the correct answer would be:
- Monthly payment (P)
- Total paid over the life of the loan
- Finance charge (Total paid - Original loan amount)
Performing the calculation gives us a monthly payment of $162.57. Multiplying this by 60 gives us a total payment amount of $9,754.20. Subtracting the original loan amount from this total payment gives us the finance charge of $1,754.20. Therefore, the correct answer to the question is option c: $162.57; $9,754.20; $1,754.20.