# 15-Year Versus 30-Year Mortgage: Which Is the Better Option? by Delbert C. Goff, Ph.D., and Don R. Cox, Ph.D.

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3 To account for the tax savings from the mortgage interest deduction, the annual after-tax payments are used. An amortization schedule is constructed on a monthly basis and the relevant variables are summed across the months to find the total annual payment, total interest paid during a year and the total principal repaid during the year. The annual aftertax payment is calculated as follows: Annual After-tax Payment = I (1 t) + PR where I is the total interest paid during a year, t is the tax rate, and PR is the principal repaid during a year. For example, the monthly payment for the 15-year mortgage is \$1, For the first year, the total annual payment is \$16,686, the total interest paid is \$11,059 and the total principal repaid is \$5,627. Therefore the annual after-tax payment is Annual After-tax Payment = \$11,059 (1 0.33) + \$5,627 = \$13,037 The annual after-tax payment for the 30-year mortgage is calculated in a similar manner yielding an after-tax payment of \$9,263 for the first year of the 30-year mortgage. The difference in the payments is calculated by subtracting the annual after-tax payment for the 30-year mortgage from the annual after-tax payment for the 15-year mortgage. An underlying assumption of the methodology is that a home buyer has the financial resources to pay the higher 15-year mortgage payment. Therefore, even if the 30-year mortgage is selected, the home buyer will be able to put an amount equal to the difference in the mortgage payments into a tax-deferred investment plan. Primary Methodology Difference The primary way in which this study differs from earlier studies is in the assumption that home buyers will be able to invest the difference in the payments in a tax-deferred investment plan such as a 401(k) or a 403(b). Since funds placed in a tax-deferred investment plan reduce the investor s current taxable income, the investor s taxes decline. For example, an investor in the 28-percent tax bracket putting \$100 into a tax-deferred investment plan will reduce his or her after-tax income by \$72 because the \$100 tax deduction will result in a tax-savings of \$28. Likewise, if the investor can afford to do without \$100 in after-tax income, he or she could place \$ into a tax-deferred investment plan. This will result in a tax savings of \$38.89 (\$ ); therefore, the investor s after-tax cash outflow will be \$100. The advantage of the tax-deferred investment plan will make a 30-year mortgage more attractive than a 15-year mortgage for many home buyers. By investing the difference between the 15-year mortgage payment and the 30-year mortgage payment in a tax deferred investment plan, home buyers may be able to save a considerable amount of money over time. For example, in the example given above, the after-tax payments for the 15-year and 30-year mortgages are \$13,037 and \$9,263, respectively. If a home 3

5 Table 1: Annual Mortgage Payments and Tax-Deferred Investment Account Balances with 15-year Mortgage and 30-Year Mortgage 5

9 Table 3: Advantage of a 30-Year Mortgage under Various Mortgage Rate Scenarios 15 Year Rate (30-15) 6% 7% 8% 9% 10% 11% 12% 0.10% \$541, \$484, \$423, \$357, \$289, \$218, \$146, % \$524, , , , , , , % \$506, , , , , , , % \$489, , , , , ,448 80, % \$471, , , , , ,981 58, % \$453, , , , , ,462 36, % \$436, , , , ,242 89,889 14, % \$418, , , , ,174 68,264 7, % \$400, , , , ,046 46,588 29, % \$381, , , , ,859 24,862 52, % \$363, , , ,677 79,615 3,086 74, % \$345, , , ,982 58,315 18,738 96, % \$326, , , ,223 36,958 40, , % \$308, , ,349 92,401 15,546 62, , % \$289, , ,132 71,515 5,921 84, ,623 Values in the body of the table represent the difference in savings account balances for the 30-year option minus 15-year option under various 15-year mortgage rates and various spread between the 30-year mortgage rates and the 15-year mortgage rates (assumes a 30-year analysis period). The final factor examined is the rate of return on investment which represents an opportunity cost for taking the 15-year mortgage option. If the expected rate of return on investment is low, then the 15-year mortgage may be the most favorable. Table 4 demonstrates the impact of changes in the rate of return on investment on the advantage to the 30-year mortgage option. This table shows that for various mortgage amounts, the higher the rate of return on investment, the greater the advantage of the 30-year mortgage option. For home buyers who can earn eight percent or more on their investments, the 30-year mortgage option appears attractive. Home buyers/investors should keep in mind that in order to earn a high return, they will have to take on riskier investments such as stocks. Therefore, it is important to bear in mind that the 30-year mortgage option calls for a long-term investment strategy. If over a 30-year period investors can earn a return equal to the average long-term rate of return on the stock market, the 30-year mortgage option appears to be the most favorable. Home buyers who are extremely conservative or who are not willing to invest in riskier investments (such as common stocks) probably will favor the 15-year mortgage option. 9

11 Summary and Conclusion This paper demonstrates that many home buyers may benefit greatly from taking a 30- year mortgage rather than a 15-year mortgage. By investing the difference between the 30-year mortgage payment and the 15-year mortgage payments in a tax-deferred investment plan, the home buyer may be able to build a sizable retirement investment account balance. The 30-year mortgage is most favorable for home buyers in high tax brackets purchasing relatively expensive homes. In addition, the 30-year mortgage option is preferred when mortgage rates are relatively low and the spread between 15-year and 30-year rates is relatively small. References 1. Paul S. Marshall, "Help Buyers Make the Right Mortgage Wish," Real Estate Today, January 1989, pp Lucinda L. McCartney, "15- Vs. 30-Year Mortgages," Consumers Digest, July/August 1989, pp Upinder S. Dhillon, James D. Shilling and Clemon F. Sirmans, "The Mortgage Maturity Decision: The Choice Between 15-Year and 30-Year FRMs," Southern Economic Journal, April 1990, pp David R. Vruwink and Dann G. Fisher, "The Effects of Income Tax Rates and Interest Rates in Choosing Between 15- and 30-Year Mortgages," The CPA Journal, November 1995, pp Delbert C. Goff, Ph.D., is an associate professor of finance at Appalachian State University in Boone, North Carolina, where he teaches undergraduate and graduate courses in financial management. He has taught several executive seminars and workshops on financial management and business valuation techniques. Don R. Cox, Ph.D., is an assistant professor of finance at Appalachian State University, where he teaches courses in investments, international finance and financial management. His research interests are in the areas of investment management and stock market efficiency. 11

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