Is a Home Mortgage an Example of TVM?

TVM stands for “time value of money.” Conceptually, it describes how money is valued differently at different times or over time. If you put $100 in a coffee can and buried it in your backyard, when you dig it up 10 years from now, it would not buy the same amount of stuff as it does today. A home mortgage is a good example of TVM.

That $100 in the coffee can offers an example of the value of money today, or present value. Inflation, or a rise in prices over time, is eating at your $100. If inflation is 2 percent per year, in just one year your $100 will only be able to buy 98 percent of what it does today. If you dig up your coffee-can cache in one year, it will have lost 2 percent of its value. The present value, or value of the buried $100 a year into the future, is only $98 today.

In a traditional 30- or 15-year mortgage, the amount of money loaned for the house is just the beginning of the equation. Because the mortgage lender or bank is lending you the money over a long period, it will collect interest on the money. The actual amount of the payments added up at the end of the mortgage term is much larger than the original loan amount. All of these payments added up over the loan term represent the TVM equation. For the mortgage lender, the original loan amount is the present value of the money made in monthly payments over the loan term.

When figuring out how much future money is worth today, TVM calculations use a discount rate. We used 2 percent inflation for our coffee-can example. We could also use a discount rate that accounted for loss of investment on the $100, such as using the $100 to purchase a certificate of deposit that pays 3 percent interest instead of burying it in the backyard. This would affect our discount rate and our TVM calculation. In reality, multiple factors weigh into the discount rate and mortgage rate calculation. A mortgage rate will primarily be based on a base borrowing rate and then compared with inflation risk and buyer default risk over the period of the loan.

In home mortgage terms, the TVM calculation is based on level payments at a certain rate over time. The buyer would like to have a large sum of money to buy a house and is willing to make monthly payments over time to repay the loan. Since that money will be paid back over time, each successive payment will be discounted back to the original loan date. Because of TVM and the interest rate applied to the loan, the amount paid will be more than the loan amount. Apply this to a 30-year mortgage with an original loan amount of $250,000 at an interest rate of 4.5 percent. A mortgage calculator yields 360 monthly payments at $1,266.71 per month. Over 30 years, a homeowner’s payments will total $456,015.60. This is $200,000 more than the original loan amount and illustrates TVM.