Suppose that you borrow [tex]$11,000[/tex] for three years at [tex]$6 \%$[/tex] toward the purchase of a car. Use [tex]$PMT =\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n r}\right]}$[/tex] to find the monthly payments and the total interest for the loan.
The monthly payment is $334.64
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total interest for the loan
(Use the answer from part (a) to find this answer. Round to the nearest cent as needed.)
Answer (2)
Calculate the total number of payments: 3 years × 12 months/year = 36 months .
Calculate the total amount paid: $334.64 × 36 = $12047.04 .
Calculate the total interest paid: $12047.04 − $11000 = $1047.04 .
The total interest for the loan is $1047.04 .
Explanation
Understanding the Problem We are given a loan of $11,000 at an interest rate of 6% for 3 years. The monthly payment is $334.64. We need to find the total interest paid on the loan.
Calculating the Number of Payments First, we need to calculate the total amount paid over the 3-year loan term. Since the payments are made monthly, there are 3 × 12 = 36 payments.
Calculating Total Amount Paid The total amount paid is the monthly payment multiplied by the number of payments: Total amount paid = Monthly payment × Number of payments = $334.64 × 36
Total Amount Paid Total amount paid = $334.64 × 36 = $12047.04
Calculating Total Interest Now, to find the total interest paid, we subtract the principal amount of the loan from the total amount paid: Total interest = Total amount paid − Principal amount = $12047.04 − $11000
Total Interest Total interest = $12047.04 − $11000 = $1047.04 Therefore, the total interest for the loan is $1047.04.
Examples
Understanding loan interest is crucial in personal finance. For example, when buying a house, knowing how much of your monthly payment goes toward interest helps you understand the true cost of the loan. This calculation also applies to student loans, business loans, and other forms of credit. By understanding the total interest paid, you can make informed decisions about borrowing and potentially save money by choosing loans with lower interest rates or shorter terms.
The total interest for the loan of $11,000 at a 6% interest rate over 3 years with monthly payments of $334.64 is $1047.04. This is calculated by determining the total amount paid and subtracting the loan principal. The total amount paid comes to $12047.04.
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