15-Year or 30-Year Mortgage?: the facts

1. A 15-year mortgage carries a lower rate and a much higher payment, and it is done in half the time. On $400,000 at 6.0% the payment is $3,375.43, against $2,528.27 at 6.5% over 30 years, and the interest over the life of each loan is $207,577 against $510,178.
2. The interest gap is not the answer, because the 30-year borrower has the difference every month to do something with. The fair comparison spends the same cash on both paths: the 15-year borrower pays the loan off and then invests the whole payment for the next fifteen years, while the 30-year borrower invests the difference from the first month.
3. With the same rate on both loans and a return equal to it, the two paths tie to the cent at every month: $1,057,680 each at year 30 in the example. Everything that separates them is the rate gap between the two loans and the gap between the 30-year rate and the return.
4. Example: $400,000 at 6.5% for 30 years or 6.0% for 15, with the $847 monthly difference invested at 7.0%. At year 15 the 15-year borrower owns the home clear, while the 30-year borrower holds $268,516 of investments against $290,237 still owed. At year 30 the 15-year path holds $1,069,883 and the 30-year path $1,033,505.
5. The return that makes the two paths equal at year 30 in the example is 7.3%. Below it the 15-year leaves more; above it the 30-year does. Choosing the 15-year is a guaranteed return on the payment difference at that break-even rate, which sits at or above the 30-year rate because the whole loan is cheaper. Choosing the 30-year is a bet that the investment beats it.
6. The arithmetic does not price the rest. The 30-year payment is a floor that can always be paid down faster, so it buys room for a lost job or a bad year. The 15-year payment is a commitment, and the equity it builds cannot be spent without selling or borrowing. Many households take the 30-year and pay it as a 15, and keep the choice.

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