Final answer:
By paying off the loan with the fifth payment, you save $710.51.
Step-by-step explanation:
To find out how much you save by paying off the loan with the fifth payment, we first need to calculate the remaining balance after the fourth payment. We are given that the balance after the fourth payment is $816.04. The loan amount is $1200 and the interest rate is 12%.
First, we need to calculate the interest for the fourth payment. The interest for each payment is calculated by multiplying the remaining balance by the interest rate. So, the interest for the fourth payment is $816.04 x 0.12 = $97.92.
Now, we subtract the interest from the payment amount to get the principal repayment for the fourth payment. The principal repayment is $106.56 - $97.92 = $8.64.
To calculate the remaining balance after the fourth payment, we subtract the principal repayment from the previous balance. The remaining balance after the fourth payment is $816.04 - $8.64 = $807.40.
Now, we need to calculate the interest for the fifth payment. The interest for each payment is calculated based on the remaining balance. The interest for the fifth payment is $807.40 x 0.12 = $96.89.
The principal repayment for the fifth payment is the remaining balance after the fourth payment minus the fifth payment interest. The principal repayment for the fifth payment is $807.40 - $96.89 = $710.51.
Therefore, by paying off the loan with the fifth payment, you save $710.51.