finance · 2 min read · United States
The 15-year mortgage saves $255,518. That is the easy half
On a $300,000 loan at 6.25% over 15 years against 7% over 30, the shorter term costs $163,008 in interest against $418,527, a saving of $255,518. The monthly payment is $2,572.27 against $1,995.91, a difference of $576.36. Comparing them properly means holding the monthly outlay equal: the 15-year borrower invests the freed payment after year 15, the 30-year borrower invests the difference throughout. At a 7% return the shorter loan is still ahead at year 30; the crossover sits near 8.2%.
Take $300,000 at 6.25% over fifteen years or 7% over thirty. The shorter loan costs $163,008 in interest and the longer one $418,527. That is $255,518 saved, and it is the number every comparison leads with.
It is also the half of the question that is not in dispute. The shorter loan always costs less interest, at every rate, on every amount. The argument is about what happens to the money you did not put into the house.
The comparison has to hold something constant
The fifteen-year payment is $2,572.27 and the thirty-year payment is $1,995.91, a difference of $576.36 a month. The usual argument says to invest that difference, and at a decent return it grows to more than the interest you saved. Stated that way it is not a comparison at all, because the two people being compared are not spending the same amount.
Hold the outlay equal instead. Both borrowers commit $2,572.27 a month for thirty years. The thirty-year borrower pays $1,995.91 of it to the bank and invests $576.36, every month, for the full three hundred and sixty. The fifteen-year borrower pays all of it to the bank until the loan clears at month 180, and then invests the whole $2,572.27 for the remaining fifteen years. Now they are comparable.
| Return | 15-year, investing after year 15 | 30-year, investing the difference |
|---|---|---|
| 5% | $687,539 | $479,682 |
| 7% | $815,312 | $703,144 |
| 8% | $890,103 | $858,985 |
| 10% | $1,066,129 | $1,302,857 |
The shorter loan is ahead at five, seven and eight percent, and behind at ten. The turn is near 8.2%. That is the whole question, and it is a question about your expected return rather than about mortgages.
Why the crossover sits above the mortgage rate
It looks as though breaking even should happen at the mortgage rate itself, around 7%, because that is what the borrowed money costs. It sits higher because the two investment streams run for different lengths. The thirty-year borrower invests a small amount for a long time; the fifteen-year borrower invests a large amount for half as long. Compounding rewards the long stream, so the return has to clear the mortgage rate by a margin before the longer loan pulls ahead.
Every figure here assumes the difference is genuinely invested, every month, for thirty years, and that the return is after tax. The invested column does not exist otherwise. A borrower who takes the longer loan and spends the $576.36 has simply paid $255,518 more for the house.
What the arithmetic will not tell you
- A committed $2,572.27 is riskier than a committed $1,995.91, and the arithmetic prices none of that.
- The shorter loan forces the saving, which is worth something no table can show.
- An assumed return is an assumption. The interest saved is arithmetic.
- Where mortgage interest is deductible the comparison moves again.
Which is to say the calculation settles less than it appears to. It tells you what you give up by choosing either one, at a return you have to supply yourself, and the choice between them is not an arithmetic choice.