How this comparison works
Enter up to three mortgages and the calculator follows each one month by month. For every loan it works out the monthly payment with the standard amortization formula, adds PMI while your balance is above 80% of the home price, and keeps a running total of the cash you have paid: your down payment on day one, then every payment after that. The chart draws those running totals on top of each other, so the point where two lines cross is the exact month one loan becomes cheaper than the other.
The formulas, and what every term means
payment = P × r ÷ (1 − (1 + r)−n)
cash paid after month k = down payment + (payment + PMI) summed over months 1 to k
| Term | Meaning |
|---|---|
| P | The amount borrowed: home price minus down payment |
| r | Monthly interest rate: the annual rate ÷ 12 ÷ 100 |
| n | Number of monthly payments: years × 12 |
| Cash paid | Everything you have paid on the loan so far, including the down payment. Tax, insurance and HOA are left out of this line because they are the same for the same house. |
| Break-even month | The first month at which one loan's cash paid passes the other's |
For the full derivation of the payment formula see the mortgage calculator.
Worked example 1: 30 years or 15 years, with the break-even by hand
A $400,000 home with $80,000 down (a $320,000 loan). The 30-year loan uses 6.5% and we assume a lower 5.9% for the 15-year loan. Your own quotes will differ.
| 30 years at 6.5% | 15 years at 5.9% | |
|---|---|---|
| Monthly principal and interest | $2,022.62 | $2,683.08 |
| Total interest | $408,142 | $162,955 |
| Total cash paid, including down payment | $808,142 | $562,955 |
To find the break-even month by hand:
- The 15-year borrower stops paying after month 180. Their loan payments total $2,683.08 × 180 = $482,955.
- The 30-year borrower's payments grow by $2,022.62 every month.
- The 30-year loan becomes the more expensive one when $2,022.62 × months passes $482,955.
- $482,955 ÷ $2,022.62 = 238.78, so the crossover is month 239 (19 years, 11 months).
Until then the 30-year loan has cost you less cash. After that it costs more, and by the end it has cost $245,187 more in total. If you expect to keep the loan longer than about 20 years, the 15-year loan is cheaper overall, provided you can carry the extra $660 a month.
Worked example 2: 5% down or 20% down?
The same $400,000 home on a 30-year loan at 6.5%, with either $20,000 down (5%, so PMI applies) or $80,000 down (20%).
| 5% down | 20% down | |
|---|---|---|
| Loan amount | $380,000 | $320,000 |
| Monthly principal and interest | $2,401.86 | $2,022.62 |
| Monthly PMI | $158.33 | $0.00 |
| Months of PMI | 124 (10 years, 4 months) | 0 |
| Total interest | $484,669 | $408,142 |
| Total cash paid, including down payment | $904,302 | $808,142 |
The 5% down buyer keeps $60,000 of cash but pays $538 more each month, and their total cost passes the 20% down buyer after month 112 (9 years, 4 months). By the end they have paid $96,160 more. Whether that is worth it depends on what you would do with the $60,000: this calculator counts dollars paid, not what invested cash could earn.
Worked example 3: three terms at once
Same house, 20% down, with a 30-year loan at 6.5%, a 20-year loan at 6.2% and a 15-year loan at 5.9%.
| 30 years | 20 years | 15 years | |
|---|---|---|---|
| Monthly principal and interest | $2,022.62 | $2,329.65 | $2,683.08 |
| Total interest | $408,142 | $239,117 | $162,955 |
| Total cash paid | $808,142 | $639,117 | $562,955 |
The 30-year loan costs more than the 20-year loan after month 277 and more than the 15-year loan after month 239. The 20-year loan costs more than the 15-year loan after month 208. Each step to a shorter term raises the payment but lowers the total. A middle term is a common compromise when the 15-year payment is too tight.
How the 15-year rate discount changes the break-even
The 30-year loan stays at 6.5%. The 15-year rate is lower by the amount shown:
| 15-year rate | Monthly payment | Break-even month | Total saved by month 360 |
|---|---|---|---|
| 6.5% | $2,787.54 | 249 (20.8 yrs) | $226,385 |
| 6.25% | $2,743.75 | 245 (20.4 yrs) | $234,267 |
| 6% | $2,700.34 | 241 (20.1 yrs) | $242,081 |
| 5.75% | $2,657.31 | 237 (19.8 yrs) | $249,826 |
| 5.5% | $2,614.67 | 233 (19.4 yrs) | $257,502 |
A bigger discount means the 15-year loan pulls ahead sooner and saves more. Even with no rate discount, the shorter loan wins on total cost, because you stop paying interest 15 years earlier.
Reading the chart
- Total cash paid starts at each loan's down payment and climbs by the monthly payment. A steeper line is a higher payment. A line that goes flat has finished paying.
- Where lines cross is the break-even month. The dashed markers show it.
- Loan balance shows how fast each loan is paid down. Shorter loans fall to zero sooner.
- Move your pointer or finger across the chart for the exact numbers at each month.
Common mistakes to avoid
- Comparing only the monthly payment. The lowest payment is often the most expensive loan overall.
- Ignoring how long you will stay. If you will sell in five years, the break-even may never arrive.
- Forgetting the down payment. It is real cash, so count it.
- Using a rate you have not been quoted. Rates depend on your credit, loan size and market. Compare real offers.
- Overstretching for a short term. Choose a payment you can keep up in a tough year, not just a good one.
What is not included
Closing costs, points, adjustable rates, FHA and VA insurance, changes in tax or insurance over time, home price appreciation, and what your money could earn if invested instead are not modeled. This is a planning tool, and your lender's Loan Estimate is the authoritative source.
Sources and review
The payment formula is the standard fixed-rate amortization formula, unit-tested against closed-form results. The break-even month is tested against an independent calculation. The Consumer Financial Protection Bureau says shorter loan terms generally save money overall but have higher monthly payments, and that a shorter term usually has a lower interest rate, by as much as a full percentage point (CFPB: understand the different kinds of loans available). It also cautions that the exact difference depends on the specifics, which is why this calculator lets you enter both rates. For more buyer guidance see the CFPB's Owning a Home tools. Last reviewed September 2026. To compare lender quotes with points, fees and credits, use the loan offer comparison calculator. Read about our methodology. Then check the full monthly payment in the mortgage calculator or what you can afford with the house affordability calculator.