Question

Suppose that you borrow 14,000 for five years at 8% toward the purchase of a car . Find the monthly payments and total interest for the loan. Do not round until the final answer .

Answer 1

To calculate the monthly payments, we can use the formula for the present value of an annuity:

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

where P is the loan amount, r is the interest rate per period, A is the monthly payment, and n is the total number of periods.

First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:

r = 0.08 / 12 = 0.00666667

Next, let's calculate the total number of periods over the life of the loan:

n = 5 * 12 = 60

Now we can plug in the values and solve for A:

14,000 = (0.00666667 * A) / (1 - (1 + 0.00666667)^(-60))

A = 276.242

So the monthly payment is $276.24 (rounded to the nearest penny).

To find the total interest, we can simply subtract the amount borrowed from the total amount paid over the life of the loan:

Total interest = (monthly payment * number of payments) - amount borrowed
= (276.242 * 60) - 14,000
= 1,574.52

So the total interest paid over the life of the loan is $1,574.52 (rounded to the nearest penny).