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 = $

the monthly interest charge on the $17,000 loan is

(.07/12)(17000) = 99.17

Since the interest is paid every month , the outstanding balance will remain at $17,000.

So we need to set up a monthly payment which will accumulate to 17,000 at the end of 5 years, using the 12% of the sinking fund
i = .12/12 = .01
n = 5(12) = 60

paym( 1.01^60 - 1)/.01 = 17000
paym = 208.16

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

(An interesting addition to the problem would be to calculate the actual effective interest rate of the loan)

Please If you can. 307.33 is coming up as the wrong answer.

You may have forgotten that the number is 170000 not 17000. Try changing it and the answer will be correct.

Late, I know but the answer is 3073.23

To find the total monthly payment, we need to add the interest payment and the sinking fund payment together.

First, let's find the interest payment.
The interest payment is the interest on the loan that needs to be paid monthly. The formula to calculate the interest payment can be found using the formula for the compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the loan (amount to be paid back)
P = the principal (initial amount borrowed)
r = the annual interest rate (expressed as a decimal)
n = the number of compounding periods per year
t = the number of years

In this case:
P = $170,000
r = 7% (0.07 as a decimal)
n = 12 (monthly compounding)
t = 5

Using the formula, we can calculate the future value of the loan (A):
A = 170000(1 + 0.07/12)^(12*5)
A ≈ 222570.21

Now, let's find the sinking fund payment.
The sinking fund payment is the amount the company needs to deposit each month in order to accumulate enough money to repay the loan at the end of 5 years. The formula to calculate the sinking fund payment is similar to the formula for the compound interest:

A = P(1 + r/n)^(nt)

In this case:
P = the sinking fund payment
r = 12% (0.12 as a decimal)
n = 12 (monthly compounding)
t = 5

We know that the future value of the sinking fund should be equal to the future value of the loan:
A = P(1 + 0.12/12)^(12*5)
222570.21 = P(1 + 0.12/12)^(12*5)

Now, let's solve for P:

P = 222570.21 / (1 + 0.12/12)^(12*5)
P ≈ 497.895

Now, we can find the total monthly payment by adding the interest payment and the sinking fund payment:

Total monthly payment = Interest payment + Sinking fund payment
Total monthly payment ≈ 497.895 + 497.895
Total monthly payment ≈ $995.79

So, the total monthly payment is approximately $995.79.