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 = $

This is what I came up with but it is wrong. Can anyone tell me where I went wrong?

If the monthly interest charge on the $17,000 loan is: (.07/12)(17000) = 99.17

then interest is paid every month , then outstanding balance should remain at $17,000.

So I were to set up a monthly payment which would accumulate to 17,000 at the end of 5 years, using the 12% of the sinking fund I would have: i = .12/12 = .01 & n = 5(12) = 60

payment (1.01^60 - 1)/.01 = 17000; so payment = 208.16

So my total monthly payment needed to discharge the loan is: 208.16 + 99.17 = $ 307.33

Only the answer is coming up as wrong.

I am reworking the problem .. I see one of my problems .. 17,000 is supposed to be 170,000. Re working problem with correct numbers now

using the 170,000 instead of 17,00 came up with 3073.23 which is correct.

In your calculation, you made a mistake in determining the sinking fund payment. Let's break down the correct calculation:

Step 1: Calculate the monthly interest payment for the loan.
The nominal annual rate is 7%, which is compounded monthly. Therefore, the monthly interest rate is (7% / 12) = 0.5833%. The loan amount is $170,000. So, the monthly interest payment is (0.5833%)(170,000) = $991.67.

Step 2: Calculate the sinking fund payment needed to repay the loan.
The nominal annual interest rate for the sinking fund is 12%, compounded monthly. Converting it to a monthly interest rate, we get (12% / 12) = 1%. The time period for the sinking fund is 5 years, which is equivalent to 60 months. Using the sinking fund formula:

Payment = (1 - (1 + r)^(-n)) / r

where r is the monthly interest rate (1%) and n is the number of months (60), we can calculate the sinking fund payment.

Payment = [(1 - (1 + 1%)^(-60)) / 1%] = $3,180.96

Step 3: Calculate the total monthly payment.
The total monthly payment is the sum of the monthly interest payment and the sinking fund payment.

Total monthly payment = $991.67 + $3,180.96 = $4,172.63

Therefore, the correct total monthly payment needed to discharge the loan is $4,172.63.