Can someone please explain how this problem is laid out to solve.A company borrows $170000, which will be paid back to the lender in one payment at the end of 5 years. The company agrees to pay monthly interest payments at the nominal annual rate of 7% compounded monthly. At the same time the company sets up a sinking fund in order to repay the loan at the end of 5 years. The sinking fund pays interest at an annual nominal interest rate of 12% compounded monthly. Find the total amount of the monthly payments, that is, the sum of the interest payment and the sinking fund payment.
Total monthly payment = $
done, see your previous post
To find the total monthly payment, we need to break down the problem and calculate the interest payment and the sinking fund payment separately.
Let's start with the interest payment:
1. First, we need to calculate the monthly interest rate for the loan. The nominal annual rate is given as 7%, so we divide it by 12 to get the monthly interest rate:
Monthly interest rate = 7% / 12 = 0.07 / 12 = 0.00583
2. Now, we can calculate the interest payment using the formula for monthly compound interest:
Interest payment = Loan amount * Monthly interest rate
Interest payment = $170,000 * 0.00583
Moving on to the sinking fund payment:
1. We need to calculate the monthly interest rate for the sinking fund. The nominal annual rate is given as 12%, so we divide it by 12 to get the monthly interest rate:
Monthly interest rate = 12% / 12 = 0.12 / 12 = 0.01
2. The sinking fund payment is the amount needed to accumulate in the sinking fund over 5 years to repay the loan. We can use the future value formula for monthly compound interest to calculate it:
Sinking fund payment = Loan amount * (Monthly interest rate / (1 - (1 + Monthly interest rate)^(-n)))
where n is the number of months (60 in this case, as 5 years = 60 months)
Sinking fund payment = $170,000 * (0.01 / (1 - (1 + 0.01)^(-60)))
Finally, we can calculate the total monthly payment by adding the interest payment and the sinking fund payment together:
Total monthly payment = Interest payment + Sinking fund payment
By plugging in the values and performing the calculations, you will get the final answer for the total monthly payments.