UPDATE: I updated the formula due to an error on my part that was caught by Brad of Analyzing Wealth. Thanks for the catch, Brad!
Did you know that your mortgage may not be as expensive as you think it is? It’s true. If you have a mortgage with a fixed interest rate, which holds your payment constant, your mortgage is cheaper than you think it is.
Say you take out a 30-year $200,000 mortgage at a fixed rate of 6.5%. Your monthly payment would be $1,264.14. Your total payments over the life of this mortgage would be $455,089 of which $255,089 would go to pay interest. However, that’s not entirely accurate because we aren’t factoring in inflation.
Normally when we talk about inflation, we talk about the gradual decrease in the purchasing power of a dollar. Although inflation works to our disadvantage when it comes to purchasing power, the opposite is true when it comes to paying off a mortgage (or pretty much any type of loan).
If inflation averages 3% per year, in 10 years, the $1,264.14 payment would have about $941 in purchasing power. In other words, had the mortgage payment increased with the inflation rate, the payment would be nearly $1,700 per month. However, the mortgage payment is still just $1,264.14.
I put together a spreadsheet to calculate the inflation-adjusted cost of the mortgage used in this example. To make the calculation I simply discounted each payment by the periodic inflation rate, which was .2466%. Then I summed all the discounted payments to arrive at the inflation-adjusted cost of the mortgage. The formula for discounting a payment (also called a cashflow) looks like this:
Payment ÷ (1 + i)n
Payment = $1,264.14
i = inflation rate of 3% or .03 raised to 1/12 since there are 12 payments per year
n = number of the payment
So, the first discounted cashflow looks like this:
$1,264.14 ÷ (1 + .002466)1
$1,264.14 ÷ 1.002466
This calculation is really easy to perform with the aid of a spreadsheet. Anyway, I came up with an inflation-adjusted total cost of $301,398 for this mortgage compared to $455,089 before the inflation adjustment.
The bottom line: mortgages aren’t as expensive as we think they are after we figure in the effects of inflation. This is especially important to think about when trying to decide between renting or buying. What are the chances of not facing a rent increase over 30 years?
Average vs. Geometric Average