Sheet Metals has an outstanding loan that calls for equal annual payments of $12,600.47 over the life of the loan. The original loan amount was $72,000 at an APR of 8.15 percent. How much of the third loan payment is interest?
$5,868.00
$4,725.89
$4,896.48
$5,009.16
$4,687.53
My name is sam and no share answer
To calculate the amount of interest in the third loan payment, we'll need to determine the remaining loan balance after the second payment.
We know that the loan amount was $72,000, and the equal annual payments are $12,600.47.
First, we'll calculate the annual interest rate by dividing the APR by 100:
Annual interest rate = 8.15% / 100 = 0.0815
Next, we'll calculate the number of payments required to repay the loan. Since the payments are made annually, this will be the same as the number of years:
Number of payments = Number of years = 72,000 / 12,600.47 ≈ 5.714
Since the total number of payments is not a whole number, we'll need to split the remaining balance into partial payments. In this case, we'll split the remaining balance in proportion to the number of full payments made.
After the second payment, two full payments have been made, leaving 5.714 - 2 = 3.714 payments remaining.
We can calculate the remaining balance by subtracting the amount paid from the original loan amount.
Remaining balance = Original loan amount - (Number of payments made × Payment amount)
= 72,000 - (2 × 12,600.47) = 46,799.06
To calculate the interest portion of the third payment, we'll multiply the remaining balance by the annual interest rate.
Interest = Remaining balance × Annual interest rate
= 46,799.06 × 0.0815 = $3,811.66 (approximately)
Therefore, the correct answer is $4,687.53, which is the closest option to the calculated interest of $3,811.66.
To determine the amount of the third loan payment that is interest, we first need to calculate the total interest paid over the life of the loan.
We can start by calculating the annual interest payment. The APR (Annual Percentage Rate) is 8.15 percent, which is the annual interest rate. To find the annual interest payment, we multiply the original loan amount by the annual interest rate:
Annual interest payment = Original loan amount * Annual interest rate
= $72,000 * 0.0815
= $5868
Since the loan calls for equal annual payments, we know that the interest amount for each payment will be the same.
Now, let's calculate the principal portion of each payment. The annual payment is given as $12,600.47, and we know that the interest payment is $5,868.00. So, the principal payment for each year would be:
Principal payment = Annual payment - Interest payment
= $12,600.47 - $5,868.00
= $6,732.47
The loan has a total of 3 payments, and we want to find the amount of interest in the third payment.
The interest portion of the third payment can be calculated by multiplying the interest payment by the number of payments made:
Interest portion of the third payment = Interest payment * Number of payments made
= $5,868.00 * 3
= $17,604.00
Since the interest payment is the same for each year, the answer is $5,868.00.
Therefore, the correct answer is :
$5,868.00