636 CHAPTER 10 Consumer Mathematics By repeatedly using the simple interest formula month to month on the unpaid balance, you could calculate the principal and the interest for all the payments, which is a tedious task. However, a list containing the payment number, payment on the interest, payment on the principal, and balance of the loan can be prepared using a computer. Such a list is called a loan amortization schedule . One way to obtain an amortization schedule is by using a computer spreadsheet program. Another way is to access an amortization “calculator” program on the Internet or on a smartphone app. A part of the amortization schedule for the Martins’ loan in Example 3 is given in Table 10.5. This schedule was generated from an Internet site called Monthly Mortgage Payment Calculator (HSH.com). c) To determine the amount of the first payment that is applied to the principal, subtract the amount of interest on the first payment from the monthly principal and interest payment. We will use the simple interest formula, i prt, = to determine the interest on the first payment. i prt $211,650 0.04 1 12 $705.50 = = × × ≈ Now subtract the interest for the first month from the monthly principal and interest payment. The difference will be the amount paid on the principal for the first month. $1010.45 705.50 − $304.95 Now try Exercise 25 Monthly principal and interest payment Interest paid for the first month Principal paid for the first month Thus, the first monthly principal and interest payment consists of $705.50 in interest and $304.95 in principal. The $304.95 is applied to reduce the outstanding balance due on the loan. Thus, the balance due on the loan after the first monthly payment is made is $211,650.00 $304.95, − or $211,345.05. 7 MATHEMATICS TODAY Home Equity Loans As you make monthly payments and pay off the principal you owe on your home, you are said to be gaining equity in your home. Equity is the difference between the appraised value of your home and your loan balance. This equity can be used as collateral in obtaining a loan. Such a loan is referred to as a home equity loan or a second mortgage . One advantage of home equity loans over other types of loans (such as installment loans) is that the interest charged on a home equity loan is often tax deductible on federal income taxes. Home equity loans are commonly used for home improvements, for bill consolidation, or to pay for college education expenses. Why This Is Important Home equity loans often have many advantages over other loan sources such as installment loans or credit cards. Table 10.5 Amortization Schedule Annual % Rate: 4.0 Loan: $211,650 Periods: 360 Monthly Payment: $1010.45 Term: Years 30, Months 0 Payment Number Interest Principal Balance of Loan 1 $705.50 $304.95 $211,345.05 2 $704.48 $305.97 $211,039.08 3 $703.46 $306.99 $210,732.10 4 $702.44 $308.01 $210,424.09 11 $695.18 $315.27 $208,239.09 12 $694.13 $316.32 $207,922.77 119 $558.84 $451.61 $167,199.37 120 $557.33 $453.12 $166,746.25 239 $337.17 $673.28 $100,477.79 240 $334.93 $675.52 $99,802.27 359 $6.70 $1003.75 $1007.09 360 $3.36 $1007.09 $0.00
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