Reiny the answer 307.33 you posted at the bottom is coming up incorrect. please if you can help i would be very grateful. 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 = $

Finance - Loans problem - Reiny, Tuesday, March 31, 2015 at 8:45pm

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)

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.

To calculate the correct total monthly payment, we need to find the sinking fund payment that will accumulate to $17,000 at the end of 5 years using the 12% annual nominal interest rate compounded monthly.

Let's break it down step-by-step:

1. Convert the annual nominal interest rate of 12% to a monthly nominal interest rate:
Monthly nominal interest rate = 12% / 12 = 1% = 0.01

2. Calculate the number of compounding periods:
Number of compounding periods = 5 years * 12 months/year = 60 months

3. Use the sinking fund formula to find the monthly payment (PMT) needed to accumulate $17,000:
PMT = (1.01^60 - 1) / 0.01 * X = 17000
(1.01^60 - 1) * X = 17000
X = 17000 / (1.01^60 - 1)
X ≈ 17000 / 1.8221188
X ≈ 9330.954890

4. Round the sinking fund payment to two decimal places:
Sinking fund payment ≈ $9330.95

5. Calculate the monthly interest charge on the $170,000 loan at a nominal annual interest rate of 7%, compounded monthly:
Monthly interest charge = (0.07/12) * 170000
Monthly interest charge ≈ $991.67

6. Calculate the total monthly payment:
Total monthly payment = Monthly interest charge + Sinking fund payment
Total monthly payment ≈ $991.67 + $9330.95
Total monthly payment ≈ $10322.62

Therefore, the correct total monthly payment, including the interest payment and sinking fund payment, is approximately $10,322.62.