The cost of a new car is $16,000, which can be financed by

paying $3000 down $300 per month for 60 months.
Use the actuarial method to find the unpaid interest.
Instead of making the thirty-sixth payment, the borrower
decides to pay the remaining balance and terminate the loan
for the car.
How much interest is saved by repaying the loan early?

To find the unpaid interest using the actuarial method, we first need to calculate the total amount that will be paid over the 60-month period.

The down payment is $3000, and the monthly payment is $300 for 60 months. So the total amount paid over 60 months would be:

$3000 (down payment) + ($300/month * 60 months) = $3000 + $18,000 = $21,000

Now, to find the unpaid interest, we subtract the original cost of the car from the total amount paid:

Unpaid interest = Total amount paid - Cost of the car
Unpaid interest = $21,000 - $16,000 = $5,000

Therefore, the unpaid interest using the actuarial method is $5,000.

To calculate the interest saved by repaying the loan early, we need to determine the remaining balance at the time of repayment if the borrower decides not to make the thirty-sixth payment.

Since the borrower has made 35 payments of $300 each, the remaining number of payments would be 60 - 35 = 25 months.

To calculate the remaining balance, we can use the loan balance formula:

Remaining balance = Principal - (Payment amount * Present value factor)

The present value factor can be found using an actuarial table or a financial calculator. For 25 months at a 5% interest rate, the present value factor is approximately 0.804.

Using this information, we can calculate the remaining balance:

Remaining balance = $16,000 - ($300 * 0.804) = $16,000 - $241.20 = $15,758.80

To calculate the interest saved, we subtract the remaining balance from the original cost of the car:

Interest saved = Cost of the car - Remaining balance
Interest saved = $16,000 - $15,758.80 = $241.20

Therefore, the interest saved by repaying the loan early is $241.20.