Why 26 half-payments beat 12 whole ones
A year contains 52 weeks, so it contains 26 fourteen-day periods. If you send half your mortgage payment every fourteen days, you send 26 halves — the equivalent of 13 monthly payments — instead of 12. That thirteenth payment arrives after the interest for the period has already been taken, so essentially all of it lands on principal.
The effect compounds. A smaller balance accrues less interest next period, which leaves more of the following payment available for principal, which shrinks the balance further. On a 30-year loan that feedback loop is worth several years of payments. On a 15-year loan, where the balance is already falling fast, it is worth considerably less.
There is a second, smaller effect that people often miss. Even ignoring the extra annual payment, half your money arrives two weeks earlier than it would under a monthly schedule, so it stops accruing interest two weeks sooner. This is why a true biweekly schedule finishes marginally ahead of a monthly schedule with one twelfth added — the two are close, but not identical.
Both effects depend entirely on one thing: your servicer must credit each half-payment to the balance on the day it arrives. If it holds the first half in a suspense account and posts one normal monthly payment on the due date, you have gained nothing at all except the discipline of paying more often.
The formula, and the two rates involved
Start with the standard amortised payment. Your monthly payment M comes from the principal P, the monthly periodic rate r = annual rate ÷ 12, and the number of payments n:
M = P·r / (1 − (1 + r)−n)
The biweekly half-payment is simply M ÷ 2. But the schedule it drives uses a different periodic rate. Interest on a mortgage accrues by the day, and a fourteen-day period is 14/365 of a year, so lenders running a genuine biweekly programme charge i = annual rate ÷ 26 per period. That is slightly less than half the monthly rate — annual ÷ 26 versus annual ÷ 24 — which is exactly what you would expect, because 26 periods fit into the year where 24 half-months would not.
From there the schedule is a straight amortisation. Each period, interest of balance × i is taken, the remainder of the half-payment reduces the balance, and the process repeats until the balance reaches zero. The number of half-payments required has a closed form:
k = −ln(1 − i·P / (M/2)) / ln(1 + i)
Divide k by 26 for years, or multiply by 12/26 for months. One useful consequence of this expression: because M is proportional to P, the ratio i·P / (M/2) does not depend on the loan size at all. The time you save is a function of the rate and the term only. A $180,000 loan and a $900,000 loan at the same rate and term both finish the same number of months early — only the dollars differ.
This calculator does not use the closed form directly. It amortises both schedules period by period, so that the final partial payment, the exact interest accrual and the year-end balances all reflect what a servicer would actually post.
Worked example: $200,000 at 6% over 30 years
Take a $200,000 balance at a 6% note rate with 30 years to run.
- Monthly rate. r = 6% ÷ 12 = 0.005, and n = 30 × 12 = 360.
- Monthly payment. (1.005)−360 = 0.166042, so 1 − 0.166042 = 0.833958. Then M = 200,000 × 0.005 ÷ 0.833958 = $1,199.10. That matches the published factor of 5.99551 per $1,000 borrowed: 5.99551 × 200 = 1,199.10.
- Half-payment. 1,199.10 ÷ 2 = $599.55, sent every fourteen days.
- Biweekly rate. i = 6% ÷ 26 = 0.00230769 per period.
- Periods to payoff.
i·P= 0.00230769 × 200,000 = 461.54. Divide by the half-payment: 461.54 ÷ 599.5505 = 0.769807. Then k = −ln(0.230193) ÷ ln(1.00230769) = 1.468839 ÷ 0.00230503 = 637.2 periods, so the 638th half-payment finishes it. - Convert to months. 638 × 12 ÷ 26 = 294.5 months, or 24 years 6 months. Against 360 months, that is about 65 months — five and a half years — earlier.
- Interest. The monthly schedule pays 1,199.10 × 360 = $431,676, of which $231,676 is interest. The biweekly schedule pays roughly 599.5505 × 637.2 = $382,050, of which about $182,050 is interest. The saving is close to $49,600.
The equivalent extra principal is M ÷ 12 = 1,199.10 ÷ 12 = $99.93 a month. Adding that to a normal payment produces a payoff at 294.5 months — within a rounding error of the biweekly result, and it costs nothing to arrange.
How to read the result
Judge a biweekly plan on three questions, in this order.
Is the acceleration real? Ask your servicer, in writing, whether each half-payment is applied to principal on receipt. If the answer is that payments are held and remitted monthly, the schedule below is fiction and your saving is zero. This is the single most common way biweekly programmes disappoint.
Does the fee eat the benefit? Third-party payment services charge setup fees and per-transaction fees. Enter the setup fee above and the calculator compares it directly with the interest avoided. A recurring fee is worse than it looks: $3.50 per half-payment over 638 periods is $2,233, which on the worked example is over 4% of the saving before you count the time value of paying it early.
Would the same money do more elsewhere? The extra thirteenth payment earns you your mortgage rate, tax-free and risk-free. At 3% that is a poor return against almost any other use of the money; at 8% it is an excellent one. If you carry credit-card debt, the comparison is not close — check what the balance is costing you with the credit card interest charge calculator before accelerating a mortgage.
One more reading point: the months saved figure is fixed by rate and term, not by loan size, but the dollars saved scale directly with the balance. A borrower with a small balance near the end of a term will see a large percentage effect on remaining interest and a small dollar effect. The amortisation schedule calculator shows where in the curve you currently sit.
Years saved by switching to true biweekly
| Note rate | 15-year term | 20-year term | 30-year term |
|---|---|---|---|
| 4% | 1.5 yr | 2.3 yr | 4.1 yr |
| 6% | 1.8 yr | 2.8 yr | 5.5 yr |
| 8% | 2.1 yr | 3.3 yr | 7.2 yr |
| 10% | 2.4 yr | 4.0 yr | 9.0 yr |
Each cell is k = −ln(1 − i·P/(M/2))/ln(1+i) converted to years and subtracted from the original term, with i = rate ÷ 26. Higher rates and longer terms both increase the gain, because both leave more interest for the extra payment to displace.
Mistakes that make a biweekly estimate wrong
- Assuming the servicer accelerates. A plan that banks each half and posts monthly saves nothing. Confirm the crediting method before you enrol or pay a fee.
- Halving the full PITI payment. Escrow for tax and insurance is not part of the loan balance. Only principal and interest should be halved; the servicer collects escrow on its own cycle.
- Paying a percentage-of-loan setup fee. Because the months saved do not depend on loan size but a percentage fee does, a percentage fee is a worse deal on a large loan than a flat one.
- Forgetting the two extra half-payments a year. Twenty-six halves is thirteen payments, not twelve. Your annual cash outflow rises by one full payment — budget for the months that contain three half-payments.
- Using it on a loan with a prepayment penalty. Rare on modern conforming mortgages, but check the note. A penalty computed on principal prepaid in a twelve-month window can be triggered by acceleration.
- Comparing against a refinance without running both. Cutting the rate and cutting the term are different levers. Price the refinance separately with the refinance break-even calculator.
Biweekly plans against the alternatives
Every acceleration strategy is the same trade in different packaging: you give up liquidity now to buy a guaranteed return equal to your note rate. What differs is flexibility and cost.
Do it yourself. Add one twelfth of the payment to each monthly instalment and instruct the servicer to apply it to principal. This reproduces almost exactly the biweekly result, costs nothing, and you can stop any month you like. The extra payment payoff calculator handles irregular contributions as well as level ones.
One lump sum a year. Sending a full extra payment each January is slightly worse than spreading it, because the money arrives later on average, but it suits people paid a bonus. The difference on the worked example is under two months.
Refinance to a shorter term. A 15-year note usually carries a lower rate than a 30-year one, so you get acceleration and a rate cut together. The cost is a contractual obligation: you cannot revert to the smaller payment in a bad year. Price the shorter term against your current note before you commit, and remember that discount points change the comparison — the points break-even calculator tells you whether buying the rate down pays back inside your expected holding period.
Recast rather than accelerate. After a large principal reduction, many servicers will re-amortise the loan over the remaining term for a small fee, lowering the payment instead of shortening the term. That is the opposite trade — it buys cash flow rather than time.
This calculator implements the ordinary fixed-rate amortised loan formula, the same convention used in Regulation Z's disclosure rules for closed-end credit. It assumes a fixed rate, equal payments, no prepayment penalty, and interest that accrues on the outstanding balance rather than being pre-computed. Adjustable-rate loans, interest-only periods and simple-daily-interest notes all behave differently; for a general payoff horizon on any level-payment debt, use the loan payoff time calculator.
Key terms
- True biweekly
- A schedule where half the monthly payment is credited to the loan every fourteen days, so 26 credits occur each year and interest accrues on a balance that falls twice a month.
- Suspense account
- A holding account where a servicer parks a partial payment until enough has accumulated to make a full instalment. Money sitting in suspense reduces no interest.
- Recast
- Re-amortising a loan over its remaining term after a large principal payment, which lowers the monthly payment while leaving the maturity date unchanged.
- Note rate
- The contractual interest rate used to compute your payment, as distinct from the APR, which folds in fees and exists for comparison between offers.