Reggie King took out a 36-month fixed installment loan of $26,000.00 at 8.5% APR to open a sporting goods store.
He began making monthly payments of $820.73.
Reggie's business does better than expected and a split second after making his 24th payment, Reggie decides to repay his loan in full.
What is the total amount due to pay off the balance? Use the actuarial method.
$9,389.85
$9,410.28
$9,479.84
$10,231.01
e
Well, Reggie certainly knows how to make a "split second" decision! Let's calculate the total amount due to pay off the balance using the actuarial method.
First, we need to calculate the remaining balance after 24 payments. We have a 36-month loan, so there are 36 - 24 = 12 payments remaining.
Using the formula for the remaining balance on a fixed installment loan, we can calculate the remaining balance:
Remaining Balance = Loan Amount - Sum of Principal Payments
Remaining Balance = $26,000 - (24 * $820.73)
Remaining Balance = $26,000 - $19,696.56
Remaining Balance = $6,303.44
Now, let's calculate the interest on the remaining balance. We know the APR is 8.5%, but we need to convert it to a monthly interest rate. So, the monthly interest rate is 8.5% / 12 = 0.0070833.
Interest = Remaining Balance * Monthly Interest Rate
Interest = $6,303.44 * 0.0070833
Interest = $44.69 (rounded to two decimal places)
Finally, we need to add the remaining balance and the interest to find the total amount due to pay off the balance.
Total Amount Due = Remaining Balance + Interest
Total Amount Due = $6,303.44 + $44.69
Total Amount Due = $6,348.13
Hmm, it seems like my calculations didn't land on any of the answer choices. Perhaps there's a mistake somewhere, or this is just another example of the unpredictable nature of clowns and math!
To find the total amount due to pay off the balance using the actuarial method, we need to calculate the remaining balance after the 24th payment.
First, calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:
Monthly interest rate = 8.5% / 12 = 0.0071
Next, calculate the remaining balance using the formula for calculating the remaining balance on an installment loan:
Remaining balance = Present value of loan - (Monthly payment * ((1 - (1 + monthly interest rate)^(-number of payments)) / monthly interest rate))
Present value of loan = $26,000.00
Monthly payment = $820.73
Number of payments = 36 - 24 = 12
Remaining balance = 26,000 - (820.73 * ((1 - (1 + 0.0071)^(-12)) / 0.0071))
Calculating the value above will give you the remaining balance after the 24th payment.
Finally, add the remaining balance to the 25th payment amount to find the total amount due to pay off the balance:
Total amount due = Remaining balance + Payment amount
Since the monthly payment amount remains the same throughout the loan term, the 25th payment amount will also be $820.73.
Total amount due = Remaining balance + Payment amount = Remaining balance + $820.73
By solving the equation, you will find the correct option from the given choices.
To find the total amount due to pay off the balance, we need to calculate the remaining principal amount after making 24 monthly payments and then add any accrued interest.
To calculate the remaining principal amount after making 24 monthly payments, we'll subtract the total amount paid from the original loan amount:
Remaining Principal = Original Loan Amount - Total Amount Paid
Original Loan Amount = $26,000.00
Total Amount Paid = monthly payment * number of payments
= $820.73 * 24
= $19,696.52
Remaining Principal = $26,000.00 - $19,696.52
= $6,303.48
Next, we need to calculate the accrued interest. We'll use the actuarial method to calculate the interest on the remaining principal for the remaining term of the loan.
Interest = Remaining Principal * Monthly Interest Rate * Remaining Number of Months
Monthly Interest Rate = APR / 12
APR = 8.5%
Remaining Number of Months = Total Number of Months - Number of Payments
Total Number of Months = 36
Number of Payments = 24
Remaining Number of Months = 36 - 24
= 12
Monthly Interest Rate = 8.5% / 12
= 0.70833% (converted to decimal)
Interest = $6,303.48 * 0.70833% * 12
= $53.37
Finally, we'll add the remaining principal and the accrued interest to find the total amount due to pay off the balance:
Total Amount Due = Remaining Principal + Interest
= $6,303.48 + $53.37
= $6,356.85
Therefore, the total amount due to pay off the balance is $6,356.85.
None of the provided answer options match this amount, so it seems there may be an error in the given answer choices or calculations.