Payment on the 15-year loan
$3,535.20
Two terms, two rates, and one number that actually decides between them: the return at which the shorter loan's head start is overtaken. Enter your own figures and both rates from the same week.
Principal and interest on the loan only; escrow items are excluded from both payments, as they are identical under either term. The invested balances ignore fees, taxes and the drag of a taxable account, and they assume a constant annual return that is supplied by you rather than forecast by this page. A negative advantage means the 15-year path is still ahead at year 30.
| Annual return assumed | 15-year path at year 30 | 30-year path at year 30 | Advantage, in dollars |
|---|---|---|---|
| 4% a year | $869,980 | $531,423 | -338,557 |
| 5% a year | $944,921 | $637,248 | -307,673 |
| 6% a year | $1,028,103 | $769,142 | -258,962 |
| 7% a year | $1,120,526 | $934,113 | -186,413 |
| 8% a year | $1,223,316 | $1,141,146 | -82,170 |
| 9% a year | $1,337,742 | $1,401,772 | 64,031 |
Almost every side-by-side of these two terms does the same thing: it adds up the interest over each term, subtracts one from the other, and reports the difference. On $400,000 at 6.73% over 15 years against 7.40% over 30, the 15-year loan costs $236,337 in interest and the 30-year loan costs $597,027, a difference of $360,690.
That number is correct, and it is not a decision. The two totals cover different lengths of time and different monthly obligations, so subtracting one from the other compares 15 years of higher payments with 30 years of lower ones and calls the gap a cost. It has one more flaw that matters more: the comparison is only valid if the extra cash in the 30-year case sits idle for three decades. It does not have to.
The rate on the shorter term is not decoration either. A 15-year fixed-rate loan is priced off a different part of the yield curve and almost always carries a lower rate than the 30-year, which is why the defaults here use the two figures published for the same week rather than one rate applied to both terms. Lenders price the shorter loan lower because they hold the interest-rate risk for half as long; that discount is part of what a borrower gives up by choosing the longer term.
To compare the terms honestly the two options have to be made to consume the same money each month. The construct used here does exactly that.
Each month both households part with the same amount. One converts it into home equity faster and then into a portfolio later; the other keeps the mortgage and builds the portfolio earlier. At the end of year 30 the loan is retired either way, so the remaining question is simply which portfolio is larger. That is what the calculator returns.
The shape of the answer is intuitive once the construct is stated. The 30-year path has a longer investment horizon, which is an advantage, and a smaller monthly contribution to invest, which is a disadvantage. Which of those dominates depends entirely on the return: with a low return, the larger contribution wins because compounding cannot do much work; with a high return, the longer horizon wins because 30 years of compounding on a modest stream beats 15 years on a large one.
| Assumed return | 15-year path at year 30 | 30-year path at year 30 | Advantage |
|---|---|---|---|
| 4% a year | $869,980 | $531,423 | -$338,557 |
| 5% a year | $944,921 | $637,248 | -$307,673 |
| 6% a year | $1,028,103 | $769,142 | -$258,962 |
| 7% a year | $1,120,526 | $934,113 | -$186,413 |
| 8% a year | $1,223,316 | $1,141,146 | -$82,170 |
| 9% a year | $1,337,742 | $1,401,772 | +$64,031 |
$400,000 at 6.73% over 15 years against 7.40% over 30, each path consuming the same monthly outflow
On the default rates the 15-year path needs the invested cash to earn 8.61% a year before the 30-year path catches up. Below that return the shorter term wins; above it the longer term wins. The crossover is not a subtle boundary either: at 4% the 15-year path is $338,557 ahead, and at 9% the 30-year path is $64,031 ahead.
This is the figure to take to a decision, because it converts a comparison of two loan products into a single testable proposition: do I expect a long-run return above or below 8.61% on money I would actually invest every month, on schedule, for thirty years? Both halves of that sentence are doing work. Money that is not invested does not participate — the 30-year advantage is contingent on the contribution being made, every month, without exception.
Two further facts about the crossover are worth knowing because they move it. It falls if the two rates are closer together, since a smaller rate discount on the shorter loan means less interest avoided; and it rises if the rate gap widens, since the 30-year path then has a larger monthly difference to invest. On the defaults the gap is 0.67 percentage points, which is why a crossover near 8.6% is high enough that the 15-year term remains ahead across a wide range of plausible returns.
The practical form of this page is therefore an experiment rather than an answer. Change the return and watch the crossover move; change the two rates and watch it move again. If the crossover sits far above any return you would actually plan around, the term decision is settled by the arithmetic and the remaining questions are the ones above. If it sits inside your range of plausible returns, the decision is genuinely a judgement about your own behaviour, and the payment calculator is the place to see what each payment does to a monthly budget.
Take $400,000 at 6.73% over 15 years and 7.40% over 30. The monthly rate on the first is 6.73 ÷ 12 ÷ 100 = 0.005608, and on the second 7.40 ÷ 12 ÷ 100 = 0.006167. Over 180 and 360 months those give $3,535.20 and $2,769.52, a difference of $765.68 a month.
Interest is each total paid less the principal: 180 × $3,535.20 − $400,000 = $236,337, and 360 × $2,769.52 − $400,000 = $597,027.
Now value the two investment streams at 6% a year, which is 0.5% a month. The 15-year path contributes $3,535.20 for 180 months beginning in month 181, and the 30-year path contributes $765.68 for 360 months beginning in month one. Applying the ordinary annuity formula to each gives $1,028,103 and $769,142 — a gap of $258,962 in favour of the shorter term at that return.
A few cents of disagreement with your own working is the rounding order. A larger gap means one of the two implementations is wrong, and the corrections page explains how to report it.
This page does not advise, and the arithmetic deliberately produces a boundary rather than a recommendation. What it shows on the default figures is that the shorter term stays ahead unless the money you would otherwise invest earns more than 8.61% a year, every month, for 30 years, after fees. Whether that is a bet you want to make is a judgement about your own behaviour and risk, not a calculation. The 15-year term is also the only one of the two whose advantage does not depend on you doing something optional every month.
Because the lender carries the interest-rate risk for half as long. The defaults use 6.73% and 7.40%, which are the national averages published for the same week, so the comparison holds everything except the term constant. Rates move weekly, and the gap between the two terms widens and narrows with the shape of the yield curve, so it is worth re-entering both figures rather than assuming a fixed spread.
For the 30-year path to have any chance of finishing ahead, yes. The extra interest of $360,690 is the price of the longer term; the only compensation offered for paying it is the use of the freed-up cash. If that cash is spent rather than invested, the comparison collapses to the interest total and the 15-year term wins by construction. That is why the calculator asks for a return rather than assuming one — entering 0% shows the cost of the longer term with no investment benefit at all.
That is a third option and it is priced separately, because it keeps the lower required payment as a cushion while voluntarily paying more. The arithmetic of the interest saved is identical to the shorter term, but the obligation is smaller and can be reduced in a bad month. The extra payment calculator works out what a recurring additional principal payment removes from the schedule.
Related calculatorsMortgage payment calculator · Extra payment calculator · Refinance break-even calculator
Cluster us/mortgage · Unit us-mortgage-15-vs-30-year-calculator · Engine amortizing-loan / term-compare · Method: Both payments come from the standard amortizing equation at 180 and 360 months. Two paths are then built on the identical monthly cash outflow: the 15-year path pays the higher payment for 15 years and invests that same payment for the following 15, while the 30-year path pays the lower payment throughout and invests the difference every month for 30 years. Each stream is valued as an end-of-month annuity at the chosen annual return. The crossover return is found on a 0.01 percentage point grid.