Example 1 (continued).

Because all payments on the conventional fixed rate mortgage loan are of equal size, part of each loan payment is interest and part is repayment of principal. Currently, the interest portion of a home mortgage payment is a tax-deductible expense. Hence, home buyers usually want to determine the dollar amount of the payment each month that is interest.

Suppose that you take out the mortgage loan in Example 1 on January 1, and your first payment is at the end of January. You will make 12 payments in the current calendar year. What is the total amount in tax-deductible interest for the first year?

We calculated that the monthly payment is $1,028.61. The original principal is $100,000, and the monthly interest rate is 1%. Hence, the portion of the first payment that is interest is

0.01 x $100,000 = $1,000

Thus, the portion of the first payment that goes toward principal is

$1,028.61 - $1,000 = $28.61

The balance that you owe after your first payment is

$100,000 - $28.61 = $99,971.39.

Next, consider your second payment in February. Your monthly payment is still $1,028.61. However, the portion that is interest is based on your balance at the end of January:

.01 x $99,971.39 = $999.71

Thus, the portion of the second payment that goes toward principal is

$1,028.61 - $999.71 = $28.90

The balance that you owe after your second payment is

$99,971.39 - $28.90 = $99,942.49.

This process is quite tedious by hand. The BA II Plus enables us to perform these calculations very quickly for individual payments as well as for ranges of payments.

Steps in the BA II Plus (assuming that the data from the calculation of the mortgage payment still is stored in the financial function keys).

Press the 2nd key, then Amort.

P1 appears on the left of the display. For the first month, type 1, then press Enter.

Press the down arrow key.

P2 appears. Type 1, then press Enter (to tell the calculator that we want only payment 1).

Press the down arrow key. BAL appears. The calculator shows that the balance owed on the principal is now $99,771.3874. (The BA II Plus does not round any of the intermediate results. Hence, results from these calculations differ very slightly from the banks calculations, because they round to the penny each period.)

Press the down arrow key. PRN appears. The portion of the first payment that goes toward repayment of principal is $28.61. (The BA II Plus displays the full accuracy of the unrounded result.)

Press the down arrow key. INT appears. This amount ($1,000) is the portion of the first payment that goes toward interest.

Recall that we want to know the total interest paid in the first 12 payments. (For example, if the first payment is January, then the first 12 payments will be deductible on your income tax returns for the current year). Do the following:

Press the 2nd key, then Amort.

P1 appears on the left of the display. For the first month, type 1, then press Enter.

Press the down arrow key.

P2 appears. Type 12, then press Enter (to tell the calculator that we want the range of payments from payment 1 through payment 12).

Press the down arrow key. BAL appears. The calculator displays the balance owed on the principal is $99,637.12 after the 12th payment.

Press the down arrow key. PRN appears. The portion of the first 12 payments that goes toward repayment of principal is $362.88.

Press the down arrow key. INT appears. This amount ($11,980.47) is the portion of the first 12 payments that goes toward interest.

Suppose that we want to know the total interest paid in the second year, that is, in the next 12 months? We assumed that the first payment is in January. Hence, the second year is composed of months 13 through 24. In the Amort function, set P1 = 13 and P2 = 24. Take a moment to carry out the calculations to determine total interest paid in the second year and balance outstanding at the end.

Total interest paid in the second year is $11,934.45; the principal that is still outstanding is $99,228.22.

Similarly, for any other time period, we simply need to identify the first month and the last month, counting from the first payment. Enter these values for P1 and P2 in the Amort function. Then use the up and down arrow keys to scroll to total interest paid and balance outstanding. If we simply want to know the balance of principal outstanding at any point, let P1 = 1 and set P2 accordingly. For example, suppose that you want to know what the balance outstanding will be after 15 years (of this 30-year mortgage loan)? Take a moment to carry out the calculations.

In the Amort function, set P1 = 1 and P2 = 180 (12 months x 15 years). Then the balance outstanding will be $85,705.71.

If the first payment is some month other than January, then choose the months accordingly. For example, if the first payment is in July, then payment 6 will be in December. Hence, for tax purposes, we want to determine the total interest paid over months 1 through 6 (July through December) for the first tax year, months 7 through 18 (January through December) for the second tax year, and so forth.

IMPORTANT TIP: when you are finished with the Amort function, you must press 2nd Quit to exit it.

Balloon mortgages

Occasionally, mortgages are designed with what is called a balloon payment. For this type of mortgage, the lender calculates the mortgage payment in the same manner as illustrated in Example 1 for a standard mortgage term (e.g., 30 years). However, the terms of the loan require that the borrower repay the entire principal owed at the end of a much shorter period, typically five to seven years. This period is called the term of the balloon mortgage.

HERE IS THE PROBLEM!

Suppose that you are considering a conventional, fixed-rate 20-year mortgage loan for $250,000. The lender quotes an APR of 7%, compounded monthly; mortgage payments would be monthly, beginning one month after the closing on your home purchase. In the tenth year of your mortgage (months 109 through 120), what would be the total dollar amount of the interest paid?

Do not round at intermediate steps in your calculation.

$13,159.65

$14,064.27

$12,112.53

$15,199.56