Final answer:
The total amount of Austin's business loan was $12,300. Over 3 years, he paid $1,171.20 in interest. The actual annual interest rate cannot be determined accurately without more details, but it is clear that a larger down payment would reduce the total interest paid on the loan.
Step-by-step explanation:
Loan Calculation and Interest
To answer Austin's business loan questions, let's take it step-by-step.
a) Total Amount of the Business Loan:
Austin made a down payment of $1600 for machinery worth $13,900. So, the total amount of the business loan is:
$13,900 - $1,600 = $12,300
b) Total Interest Paid Over the 3-Year Period:
Payment per month: $374.20
Number of payments: 3 years × 12 months/year = 36 payments
Total amount paid: 36 payments × $374.20/payment = $13,471.20
Total interest paid: Total paid - Loan amount
$13,471.20 - $12,300 = $1,171.20
c) Annual Interest Rate on the Business Loan:
To determine the annual interest rate, we would generally need more information such as whether the rate was fixed or compound interest, as well as the compounding frequency. If we assume simple interest, we can use the formula I = P × r × t to back out the interest rate, but without the proper details, this calculation could be inaccurate.
d) Effect of a Larger Down Payment:
If Austin had made a larger down payment, the principal amount of the loan would be lower. This would result in him paying less in interest because there would be a smaller amount subject to the interest rate. Over time, a larger down payment reduces the total amount paid for the loan.