Question

Amortizing loans. Suppose that you take out a $200,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%, and payments on the loan are made annually at the end of each year.

1. What is your annual payment on the loan?

2. Construct a mortgage amortization table in Excel similar to Table 2.1, showing the interest payment, the amortization of the loan, and the loan balance for each year.

3. What fraction of your initial loan payment is interest? What about the last payment? What fraction of the loan has been paid off after 10 years? Why is the fraction less than half?

Answer 1

(i) Answer attached below:

(ii) The amortization table of the loan is given below:

(iii) Loan payment per annum = USD 17,436.91 _________ as calculated in part (i)

Interest payment as a part of initial loan payment = USD 12,000 _______ given in table above(ii)

Interest as a % of total loan payment = 12000 / 17436.91 = 68.82%

Interest payment as a part of last loan payment = USD 987 _______ given in table above(ii)

Interest as a % of total loan payment = 987 / 17436.91 = 5.66%

(iv) Closing balance at the end of 10 years = USD 128,337

Hence, the loan repaid = USD 200,000 - USD 128,337 = USD 71,663

This is 35.8% (=71,663 / 200,000) of the loan availed.

This amount is less than 50% because in the initial years, out of the total payment, majority share goes towards interest payment. Over the the years, as the outstanding balance reduces, the interest payable reduced and more principal is paid.