15-year vs 30-year mortgage payments

A 15-year mortgage and a 30-year mortgage are the same loan-payment problem with a different number of months. Both are fully amortising: one level payment, repeated until the balance is exactly zero. The payment is

$$M = P \times \frac{i}{1 - (1 + i)^{-n}}$$

$P$ is the amount borrowed, $i$ the monthly rate, and $n$ the number of payments: 180 or 360. Raise $n$ and $M$ falls. The total paid is $n \times M$, so the longer loan takes more off the table even while each month asks for less. Interest over the full term is that total minus $P$.

At ordinary mortgage rates, stretching the same principal from 15 years to 30 more than doubles the interest. Across ordinary mortgage rates the 15-year payment sits about 30 to 55 percent above the 30-year payment of the same size, with the gap widest when the rate is low. Those ranges are the same-rate comparison. In the United States a 15-year quote is usually a fraction of a percentage point cheaper as well, which narrows the payment gap and widens the interest gap.

The loan payment calculator is that formula with a schedule attached. This page is the comparison the two values of $n$ produce. The usual pairing here is two fixed-rate, fully amortising United States loans. A UK fixed rate that lasts two to five years and then reverts is a different product, closer to an adjustable loan than to either of these terms.

Nothing in the contract front-loads the interest. Interest is charged on the principal still owed, so the first months of any amortising loan spend most of the payment on interest simply because the balance is then at its largest. Amortisation is that split, month by month, and the split is what the term changes.

A larger payment on a shorter term leaves more after the first month's interest has been taken out, so more comes off the balance, so the next month's interest is calculated on a smaller number. The effect compounds in the borrower's favour. At 6.5 percent, the illustrative rate on the how mortgages work guide, the first payment on a 30-year loan is about 85.7 percent interest; on a 15-year loan of the same size it is about 62.2 percent. After 60 payments the 30-year has retired about 6.4 percent of the original balance and the 15-year about 23 percent. On the 30-year, principal does not overtake interest in a given payment until around payment 233, year 20 of 30. On the 15-year that crossover arrives around payment 53.

That is why five years of a 30-year mortgage can feel like no progress. A large share of what has been handed over was interest, and most of the debt is still there. The how mortgages work guide runs the same 6.5 percent schedule payment by payment. None of those percentages depend on the amount borrowed: they are properties of the rate and the term.

Three things sit around the formula, and each one moves the comparison.

The rate is not required to be the same. Lenders in the United States usually quote a 15-year fixed rate below the 30-year rate for the same borrower, because they are exposed to a rise in market rates for half as many years. The gap is a price, and it moves. A lower 15-year rate is an advantage extra payments on a 30-year loan cannot copy: prepaying a higher-rate loan still pays the higher rate.

Qualifying is a payment test. Lenders look at debt-to-income, so the higher 15-year payment supports a smaller loan on the same income, or demands more income for the same loan. That is why the 30-year is the default term in the United States. Tax and insurance collected into escrow do not change with the term, but they compete with principal and interest inside the same monthly ceiling, so they shrink the loan either payment will support.

The option is the part a 15-year cannot offer. In the United States most residential mortgages can be prepaid without a penalty. Paying extra principal on a 30-year loan shortens the term and cuts interest, which is what the mortgage payoff calculator measures, and the contracted payment stays the lower 30-year figure. Stop the extra and the loan simply takes longer; it does not miss a payment. A 15-year payment is the minimum. Copying a 15-year schedule on a 30-year loan at the same rate means paying the 15-year amount each month: the balance then clears in 180 months, with the right to drop back if the month requires it. What that copy cannot do is manufacture the 15-year rate.

Upfront fees cut the other way. Spread over 180 months they weigh more on the 15-year APR than on the 30-year one, and an early sale or refinance concentrates them on whichever term you actually served.

The 15-year is not the serious version of the 30-year, and the 30-year is not the expensive version of the 15-year. They are a higher contracted payment with less interest and fewer years of debt, against a lower contracted payment with more interest, more years, and the option to prepay.

A budget that absorbs the 15-year payment with room to spare, and a hold expected to last, is the case for writing the shorter term into the note: the rate is usually better, the schedule cannot be quietly abandoned, and the interest total is the smaller one even before that rate difference. A budget that needs the lower floor, or a household that would rather decide each month whether extra principal is what the cash should do, is the case for the 30-year. The extra can still be paid. It is not owed.

Two things the interest total does not settle. The dollars that go out over 15 years and over 30 years are dollars from different years, so adding them up is not a like-for-like comparison: money paid later is paid in money that inflation has made smaller, and money not sent to the lender could have been doing something else. Whether those next units belong on the mortgage or elsewhere is a separate question from what the two schedules cost if they are followed. How mortgages work is the mechanics; this page is the term comparison.

Which term fits turns on a payment you can carry, a hold you actually expect, and a rate you have been quoted, which is why this is educational material and not financial advice.