How extra payments shorten a mortgage
On a fixed-rate mortgage the monthly principal and interest payment is set when the loan starts. When you pay more than that amount and the lender applies the difference to principal, the balance falls faster. Next month's interest is charged on that lower balance, so a larger part of the regular payment also goes to principal, and the effect compounds month after month. The regular payment does not change; the loan simply ends sooner and costs less interest.
Each month of the payoff schedule follows four steps:
interest = B × r, whereBis the balance andris the yearly rate ÷ 100 ÷ 12.principal = (M − interest) + x, whereMis the regular payment andxis the extra amount.B = B − principal.- Stop when the balance reaches zero; the last payment is only what is left.
Without rounding, the number of months has a closed form: months = −ln(1 − r × P ÷ (M + x)) ÷ ln(1 + r), rounded up; the schedule agrees with it to within a month. The regular payment M comes from the standard level-payment formula on the original amount and term, and the calculator rounds interest to the cent each month, so its count is the one a real schedule would show. The interest saved is the interest on the regular schedule minus the interest on the faster one.
Worked example: extra payments on a published Loan Estimate
The Consumer Financial Protection Bureau's sample Loan Estimate (form H-24(B)) describes a $162,000.00 loan at a fixed 3.875% over 30 years with monthly principal and interest of $761.78. With no extra payment the calculator reproduces that schedule: a payment of $761.78, $15,773.00 of principal repaid in the first five years (the form shows $15,773), and $112,243.70 of interest over 360 payments.
Now add $100.00 to every payment from the first month:
- Month 1: interest is $523.13, and $338.65 goes to principal instead of $238.65.
- After 5 years the balance is $139,618.47 instead of $146,227.42.
- The loan is repaid after 290 payments (24 years 2 months), 5 years 10 months early.
- Total interest falls from $112,243.70 to $87,667.48: a saving of $24,576.22 for $29,000.00 of extra payments.
The saving per extra dollar is large because each early dollar of principal stops accruing interest for the rest of the term, which at the start is close to thirty years.
How much each extra amount changes
The calculator opens with $300,000.00 at 6.5% over 30 years, a regular payment of $1,896.20 and $382,636.71 of interest if nothing extra is paid. Adding a fixed amount every month from the start:
- $50.00 more a month: repaid in 27 years 10 months, $33,582.51 of interest saved.
- $100.00 more a month: repaid in 26 years, $60,995.81 of interest saved.
- $200.00 more a month: repaid in 23 years 1 month, $103,450.19 of interest saved.
- $500.00 more a month: repaid in 17 years 6 months, $179,761.68 of interest saved.
- $1,000.00 more a month: repaid in 12 years 9 months, $241,165.01 of interest saved.
Each extra step still saves money, but the time saved per extra dollar shrinks as the term gets shorter, because there are fewer months left for the saving to compound.
Starting part-way through the loan
You do not need the original loan details. Because the payment on a level-payment loan stays the same, entering today's balance and the years left gives the same regular payment, to within a few cents of rounding. For example, after ten years the default loan has $254,329.14 left; adding $200.00 a month from then on saves $39,657.95 and ends it 3 years 5 months early, compared with $103,450.19 and 6 years 11 months when the same extra starts in month one.
Biweekly payments
Paying half of the monthly payment every two weeks adds up to 26 half-payments, or 13 full payments, a year. That is the same as paying one-twelfth of a payment extra each month, $158.02 on the default loan, which repays it in 24 years 2 months and saves $87,259.03. A biweekly plan only has this effect if the lender credits each half-payment when it arrives or applies the extra to principal.
What this calculator leaves out
It covers principal and interest only. Property tax, insurance and any mortgage insurance collected with the payment are not affected by paying principal early. Some loan agreements charge a fee for paying ahead of schedule, and adjustable-rate loans change their payment when the rate resets; read your own agreement for both.
Frequently asked questions
Does paying extra lower my monthly payment?
Not by itself. The regular payment stays at $1,896.20 on the default loan and the loan ends sooner. Some lenders offer to re-amortize (recast) the loan after a large lump sum, which lowers the payment over the remaining term instead of shortening it; that is a different calculation from the one shown here.
How do I make sure the extra goes to principal?
Lenders handle amounts above the scheduled payment in different ways, for example by holding them toward the next payment. The schedule above assumes every extra amount reduces principal in the month it is paid. Your monthly statement shows how the lender applied it.
Why does an extra payment early in the loan save more than one near the end?
A dollar of principal repaid in month one would otherwise have accrued interest for the remaining term; a dollar repaid in the final years saves only a few years of interest. The comparison above between starting in month one and starting after ten years shows the difference on the default loan.
Can I model a one-time lump sum?
Not directly: the calculator models the same extra amount every month. Entering a balance reduced by the lump sum with the same years left shows what a recast would do, a lower regular payment and the same end date, because the regular payment is worked out from the balance and term you enter. Comparing that payment with your current one shows the effect of the lump sum on the monthly bill.
Is the amount saved exact?
It follows the same rounding a monthly schedule uses: interest rounded to the cent each month and the last payment settling the remainder. A lender that charges interest daily, or receives payments on different days of the month, will show slightly different cents.
Sources
- Consumer Financial Protection Bureau, sample Loan Estimate for a fixed-rate loan (form H-24(B)) — the loan amount, rate, term, monthly principal and interest and five-year principal used as the starting point of the worked example.
- Regulation Z, Appendix H to Part 1026: closed-end model forms and samples