Suppose that you borrow ​$10,000

Question

for three

years at 7​%
toward the purchase of a car. Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction

to find the monthly payments and the total interest for the loan.

Answer 1

To solve this problem, we need to understand the PMT formula for loan calculation:

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

Where:
P = principal amount (the amount of the loan)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = time (duration of the loan in years)

In this case:
P = $10,000
r = 7% (or 0.07 in decimal form)
n = 12 (monthly payments)
t = 3

Substituting these values into the formula, we get:

PMT = 10000 * (0.07/12) / (1 - (1 + 0.07/12) ^ -(12*3))

This simplifies to:

PMT = $308.77 (rounded to nearest cent)

This means that the monthly payment for the car loan will be approximately $308.77.

As for the total interest, we can calculate it as follows:

Total interest = Total amount paid - Principal
Total amount paid = PMT * n * t
Total amount paid = $308.77 * 12 * 3 = $11115.72

Therefore, the total interest = $11115.72 - $10000 = $1115.72

Hence we can conclude that the monthly repayment for the car loan will be approximately $308.77 and the total interest paid over three years will be approximately $1115.72.