6. The mathematics of mortgage loans - Part 2

The Mathematics of Mortgage Loans

In general, a mortgage loan is repaid monthly over the term of loan using the process of amortization, in which each payment contains two components: the interest that is owed on the debt outstanding and the portion of the principal that is being repaid.

An amortization table or schedule details the monthly payments, the portions that will be used to pay the accrued interest and the repayment of the principal, and the debt remaining after each payment is made over the life of the loan.

You will start by constructing an amortization schedule.

Your dream is finally coming true! Youve saved and saved and are about to become a homeowner!

After a conversation with your banker, youve agreed to a 20% down payment on your $182,188 home. To keep this problem and your calculations relatively brief, assume that the bank has offered you a mortgage loan for $145,750 that carries a 6% interest rate, semiannual payments of $26,905, and a 3-year term. Remember, the process is the same when you are preparing for either 6 semiannual payments of nearly $27,000 or 360 monthly payments of $873.85 for a 30-year conventional mortgage.

Complete the following loan amortization table by entering the correct answers.

Notes:

1.	As all values are denominated in U.S. dollars, you do not have to enter any dollar signs.
2.	Round all interest payments down to the nearest whole dollar.
3.	Rounding creates a situation in which the numbers in the loans final payment are often unequal. Notice in this problem, the ending balance for payment 6 is $2. Therefore, your final payment would actually be reduced by $2 to $26,903. In the real world, to prevent over paying, you should call the lender to learn the actual amount due.

Payment	Beginning Amount	Payment	Interest	Repayment of Principal	Ending Balance
1
2
3
4
5
6					2
Total:	-----	161,430			-----

The total of the Interest column indicates the amount of interest expected to be paid over the life of the loan, and the sum of the Payment column details the total paid ($161,430) to purchase your $145,750 home.

This is an amortized loan, because its payments contain:

Both interest and principal

Only the principal that must be repaid

Only accrued interest

The monthly payment in the loan here is influenced by 3 variables: the amount borrowed, the loans interest rate, and the term. What is the nature of the relationship between each of these variables and the size of a loans payment, everything else assumed to remain constant?

	An increase in the amount borrowed will the size of the borrowers monthly payment.
	An increase in the loans interest rate will the size of the borrowers monthly payment.
	An increase in the loans term will the size of the borrowers monthly payment.