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 = $
If the monthly interest charge on the $17,000 loan is: (.07/12)(17000) = 99.17
And the 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.
Have a 27,062 car loan payable over 6 years want to pay 3000 toward the principle what will I owe 3% financing
To find the correct total monthly payment, let's break down the calculation step by step:
1. First, calculate the monthly interest payment on the loan. The formula to calculate the monthly interest payment is (0.07/12) * $17,000, which gives us $99.17 as you correctly calculated.
2. Now, let's calculate the monthly sinking fund payment. We need to calculate the monthly payment that will accumulate to $17,000 at the end of 5 years, using an annual nominal interest rate of 12% compounded monthly.
To do this, we can use the formula for the future value of an ordinary annuity:
Payment = (1 - (1 + 0.12/12)^(-5*12)) / (0.12/12) * $17,000
Calculating this, we find that the sinking fund payment is approximately $209.82.
3. Finally, to find the total monthly payment, add the monthly interest payment and the sinking fund payment together:
Total monthly payment = $99.17 + $209.82 = $308.99 (rounded to two decimal places)
So the correct total monthly payment to discharge the loan is approximately $308.99, not $307.33 as you stated.
Please double-check your calculations to ensure you've performed the calculations accurately.