To find the total amount of the monthly payments, we need to calculate the interest payment on the loan and the sinking fund payment separately, and then add them together.
First, let's calculate the interest payment on the loan. The loan amount is $170,000 and the nominal annual interest rate is 7% compounded monthly. To find the monthly interest charge on the loan, we divide the nominal annual interest rate by 12 and then multiply it by the loan amount:
Interest payment = (7%/12) * $170,000
= (0.07/12) * $170,000
= $99.17
Since the interest is paid every month, the outstanding balance will remain at $170,000.
Next, we need to calculate the sinking fund payment. The sinking fund pays interest at an annual nominal interest rate of 12% compounded monthly. We need to find the monthly payment that will accumulate to $170,000 at the end of 5 years, using the 12% sinking fund interest rate.
Let's use the formula for the future value of an annuity:
Future Value = Payment * [(1 + interest rate)^n - 1] / interest rate
Here, the future value is $170,000, the interest rate is (12%/12) = 0.01, and the number of periods is 5 * 12 = 60.
$170,000 = Payment * [(1 + 0.01)^60 - 1] / 0.01
We can solve this equation for the sinking fund payment, Payment:
Payment = $170,000 * 0.01 / [(1 + 0.01)^60 - 1]
= $208.16
So, the sinking fund payment is $208.16.
Finally, we can find the total monthly payment by adding the interest payment and the sinking fund payment together:
Total monthly payment = $99.17 + $208.16
= $307.33
Therefore, the total amount of the monthly payments, including the interest payment and the sinking fund payment, is $307.33.