Insights From Mortgage Math

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In the last few years mortgage rates have touched lows we’ve never seen in our lifetimes and recently risen to levels not seen in over a decade.  In the initial stages of mortgages, the interest calculated is based on the mortgage rate applied to a vastly huge mortgage balance.  You might be surprised to learn that even relatively small changes in mortgage rates can have massive impact on the percentage of payments that go towards principal, the advantage of making early prepayments on the mortgage, and the value that can be financed in a loan.

By the end of the loan, almost 100% of every payment goes to principal, but early on the amount varies widely.  For example, for a 2.0% mortgage, 55 cents of every dollar in the first payment goes towards paying off principal.  For a 6.0% mortgage, only 16.6% of that first payment goes towards principal.  This means the lower the mortgage rate you lock in, the quicker you build equity.

For a 30 year fixed mortgage at the beginning of the loan, how much time does it knock off to prepay one month’s payment?  Again, the answer varies widely depending on your mortgage rate.  At the extreme of a zero percent mortgage, a month’s prepayment will reduce the term of your loan by exactly one month.  At a 2% mortgage it will knock almost two months off, while at 6% it will reduce the term by almost six months.  As mortgage rates get higher, the numbers get more extreme- at an 11% mortgage, a single month’s prepayment early on will reduce the term by over two years!  This is interesting but not very practical.  If you have resources to make very large prepayments early in a mortgage, you probably could have just made a larger down payment to begin with and locked in a much lower monthly payment.  Nevertheless, it does show that as mortgage rates rise, prepayments become much more beneficial.

Probably the most interesting variable about mortgage rates is the potential impact they could have on house prices.  Imagine a 30 year fixed mortgage with a $1,500 monthly principal and interest payment and zero down payment.  How much house will that buy?  At today’s 5% mortgage rate, that payment would finance a $279,000 loan.  At 2.75%, a rate we were seeing just a few months ago, that payment would buy a $367,000 house.  If rates jumped to 10%, a rate most of us have seen in our lifetimes, that same $1500 a month could only buy a $170,000 house. 

When mortgages are discussed, the question of paying them off early always comes up.  When we run the numbers historically, the answer is that you should not prepay a mortgage at all if you can help it, at least at these rates.  It’s difficult to find a 30 year period where the return of a reasonable investment allocation would not greatly exceed 5%.  Ultimately owning a house is far more an emotional decision than a financial one, so making choices in your mortgage for peace of mind rather than optimal dollars and cents can make sense- many of our clients pay off their mortgage even knowing it’s not likely to be an optimal financial decision. 

There is always uncertainty in real estate, and it feels like these times are more uncertain than usual.  Hopefully, these facts can help you think through your real estate decisions as mortgage rates rise and more inventory comes on the market.


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