Solve the problem.
-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.
A) $92
B) $3630
C) $1435
D) $3045

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly payment using the formula:

Monthly payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

where P is the principal amount (borrowed amount), r is the monthly interest rate (11% / 12 months = 0.0091667), and n is the total number of payments (5 years * 12 months = 60). Plugging in the values, we get:

Monthly payment = (10,000 * 0.0091667 * (1 + 0.0091667)^60) / ((1 + 0.0091667)^60 - 1) = $212.47

Now, we can calculate the total amount paid over the period of the loan by multiplying the monthly payment by the total number of payments:

Total amount paid = Monthly payment * Total number of payments = $212.47 * 60 = $12,748.20

Finally, we can calculate the total interest paid by subtracting the principal amount from the total amount paid:

Total interest paid = Total amount paid - Principal amount = $12,748.20 - $10,000 = $2,748.20

Rounding to the nearest dollar, we get $2,745, which is closest to option D: $3045. First, we need to calculate the monthly payment using the formula for a loan with equal payments:

Monthly Payment = (Loan amount x monthly interest rate) / (1 - (1 + monthly interest rate)^(-total number of payments))

Plugging in the given values, we get:

Monthly Payment = (10,000 x 0.11/12) / (1 - (1 + 0.11/12)^(-5 x 12))

Monthly Payment = $212.47

Next, we need to calculate the total amount paid over the period of the loan, which is simply the monthly payment multiplied by the total number of payments:

Total Payments = Monthly Payment x total number of payments

Total Payments = $212.47 x (5 x 12)

Total Payments = $12,748.20

Finally, we need to calculate the total interest paid, which is the difference between the total payments and the loan amount:

Total Interest = Total Payments - Loan amount

Total Interest = $12,748.20 - $10,000

Total Interest = $2,748.20

Rounding to the nearest dollar gives us $2,745. Therefore, the best choice is D, $3045.

Solve the Problem. -Sammy Borrowed $10,000 to Purchase a New Car at an Car