A company borrows $140000, which will be paid back to the lender in one payment

Question

A company borrows $140000, which will be paid back to the lender in one payment at the end of 6 years. The company agrees to pay yearly interest payments at the nominal annual rate of 5% compounded yearly. At the same time the company sets up a sinking fund in order to repay the loan at the end of 6 years. The sinking fund pays interest at an annual nominal interest rate of 6% compounded yearly. Find the total amount of the yearly payments, that is, the sum of the interest payment and the sinking fund payment. Total yearly payment = $

Explanation / Answer

If the yearly interest charge on the $140,000 loan is: (.05/6)(140000) = 1166.67

then interest is paid every month , then outstanding balance should remain at $140,000.

So I were to set up a yearly payment which would accumulate to 140,000 at the end of 5 years, using the 6% of the sinking fund I would have: i = .06/6 = .01 & n = 6

payment* (1.01^6 - 1)/.01 = 140000; so payment = 22756.77

So my total monthly payment needed to discharge the loan is:22756.77 + 1166.67 = $ 23923.44

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