Is a Home Mortgage an Example of TVM?

Say that because of inflation, money loses 1 percent of its value every year. If someone gave you $1 today, you'd have $1. But say that person promised to give you $1 a year from now. That future $1 is worth only about 99 cents in today's dollars, because by the time you get it, it will have lost 1 percent of its value. In TVM terms, then, you refer to 99 cents as the "present value" of $1 to be received a year from now.

When you take out a mortgage to buy a home, the money you borrow in a TVM equation is the present value of all the mortgage payments you're scheduled to make over the next 15 or 30 years. In finance, the price of any investment is the present value of the cash flows the investor expects to receive from the investment. In the case of your mortgage, the investor is your bank -- or whoever is lending you the dough. The lender gives you a certain amount of money with the expectation that it will collect those payments.

Every TVM calculation also involves what's called a discount rate. That's the rate at which money changes value over time. In the comparison of $1 today with $1 a year from now, the discount rate was the inflation rate: 1 percent each year. In the real world, discount rates take into account not only inflation but also the "opportunity cost of capital" -- the return investors could get on their money if they used it for something else. With a mortgage, the discount rate is simply the interest rate charged by your lender. Lenders don't just pluck rates out of the air at random; they set them based on their opportunity cost of capital, which is why mortgage rates rises when other interest rates climb.

Say you take out a $200,000 mortgage for 30 years at an interest rate of 6 percent a year. Because mortgages are paid monthly, the lender actually charges you interest at a rate of 0.5 percent a month (6 percent divided by 12 months). You'll make 360 monthly payments of $1,199.10. You can actually figure out the present value of each individual payment using the following formula, in which "p" is your payment amount, "r" is your monthly rate expressed as a decimal (so 0.5 percent equals 0.005) and "t" is the number of the individual payment: p/(1+r)^t.

Using the formula just given, you can calculate that, at the time you take out that $200,000 loan, the present value of the first payment (due in one month) is $1,199.10/1.005^1, or $1,193.13. The present value of the 360th and last payment is $1,199.10/1.005^360, or $199.10. If you were so inclined, you could do all 360 payments, then add them up. The answer you'll get is $200,000 -- the amount you borrowed and the present value of your lender's investment.