The same cash, two loans, and what each leaves behind.

The facts, in one place.

Six quotable sentences on the 15-year against the 30-year.

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.

By the expected return.

How the answer moves with the one assumption that decides it.

How the comparison works.

The lifetime interest on a 30-year loan is roughly two and a half times that on a 15-year loan at a slightly lower rate, and that figure is where most comparisons stop. It is the wrong figure, because the 30-year borrower is not asked to spend the difference; the difference is theirs every month. The only fair comparison spends the same cash on both paths. On the first, the 15-year payment goes to the loan for fifteen years and then, the loan gone, the whole payment is invested for fifteen more. On the second, the 30-year payment goes to the loan for thirty years and the difference is invested from the first month. Each path's position at any month is its investments less the balance still owed, and the tool compares them at year 15, at year 30, and at a year you choose.

Built that way, the two paths tie to the cent at every month when the two loans carry the same rate and the return equals it, because a dollar of debt retired and a dollar invested compound alike. Everything that separates them is two gaps: the rate gap between the loans, which favors the 15-year, and the gap between the 30-year rate and the return, which favors whichever is higher. The break-even return folds both into one number: the return at which the 30-year path matches the 15-year at year 30, found by bisection. Choosing the 15-year is a guaranteed return on the payment difference at that rate. What the arithmetic cannot price is the flexibility of the lower payment and the discipline the 30-year path assumes, which is that the difference is actually invested, every month, for thirty years.

Methodology.

1. Inputs. The loan amount, the 30-year and 15-year rates, the expected yearly return on the invested difference, the share of that return taken by tax each year, and the year to compare.
2. The payments. The level monthly payment on each loan from the amount, its rate, and its months; the monthly cash spent on both paths is the larger of the two.
3. The 15-year path. Each month interest accrues at the 15-year rate and the payment is applied; any cash above the payment is invested; once the loan is gone, the whole monthly cash is invested at the after-tax monthly return through month 360.
4. The 30-year path. Each month interest accrues at the 30-year rate and the payment is applied; the difference is invested at the after-tax monthly return through month 360.
5. The comparison. Investments less balance owed on each path at month 180, month 360, and the chosen horizon; the lifetime interest on each loan; principal paid down plus investments drawn as two lines.
6. The break-even return. The before-tax return at which the two positions at month 360 are equal, by bisection between minus 10 and 30 percent; none reported when no such return lies in that range.
7. Validation. The payments on $300,000 at 6 percent over 30 years ($1,798.65) and at 5.5 percent over 15 ($2,451.25), and the lifetime interest from them; equal rates and a return equal to them tie at year 15, at year 30, and at the horizon within a cent, with the break-even equal to the rate; the 15-year position at year 15 is zero; with the 15-year rate lower the break-even exceeds the 30-year rate and the paths tie at it within a dollar; a return above it favors the 30-year and below it the 15-year; and the tax drag lowers the net return and the 30-year result. A transcription error fails the build.
8. Not modeled. The mortgage interest deduction, closing costs that differ between the loans, points, mortgage insurance, refinancing later, variable rates, the chance that the difference is not invested, and the risk that the return is not the average. Hypothetical throughout. Educational, not advice.

Revision history.

The assumption tools' history.

September 7, 2026

Added should you buy points (the bought-down loan against the plain one on the same principal and term, so the position is the interest saved less the cost of the points; true break-even as the first month at or above zero beside the simple rule; the horizon verdict; the return the points earn to the horizon as the monthly-compounded rate at which their cost equals the present value of the saving plus the lower balance owed, by bisection; the largest points count that pays off within the horizon; and the seller-paid case set against the same dollars off the price).

September 7, 2026

Added two mortgage assumption tools: refinance break-even (the simple rule, closing costs over the monthly saving, beside the month-by-month count of interest paid on each loan, where total cost is the balance plus the closing costs plus the interest so far, so the new loan's position is the interest saved less the costs; the reset-the-clock effect flagged when a longer term catches up), and 15-year or 30-year mortgage (the same cash on both paths, the 15-year payment invested after the loan is gone against the difference invested for thirty years, compared at year 15, year 30, and a chosen horizon, with the break-even return by bisection).

September 7, 2026

Added three assumption tools: Roth or traditional 401(k) (the same take-home cost grown at one return and taxed at each end, so the answer turns on the two rates; the plan limit from the annual record), pay off the mortgage or invest (two month-by-month paths, the extra to the mortgage and then the freed payment invested, against the extra invested throughout, with the optional interest deduction), and how much life insurance (the present value of the income to replace as a growing annuity, plus debts, final expenses, and education, less existing coverage and savings, beside the ten-times-income rule).

September 6, 2026

Added two assumption tools: sell or keep the house (carrying costs and appreciation against rent and the return on freed equity, with the home-sale exclusion), and the long-term care cost projection (today's rate at care inflation to the start year, summed over the years of care, with the set-aside today).

September 4, 2026

First release of the longevity projection (year-by-year, spending and outside income indexed to inflation, a fixed return on the remainder, with the sustainable-spending solver) and the pension-versus-lump-sum comparison (the lump sum invested and paying the pension, with the break-even return solver).

Canonical address: https://consideratecapital.com/tools/15-or-30-year-mortgage