Why an extra $200 removes far more than $200 of debt
Extra principal works because interest on a mortgage is charged on the balance you currently owe, and nothing else. A dollar sent to principal today is a dollar that never appears in any future interest calculation — so it saves r dollars of interest next month, and again the month after, for every month that remains on the loan.
That is why the leverage looks implausible until you write it out. On the default case here — $300,000 at 6.5% with 30 years to run — adding $200 a month retires the loan 83 payments early and avoids $103,449 of interest, for roughly $55,000 of extra principal paid. Each extra dollar buys about $1.87 of avoided interest.
Two structural facts matter more than most people realise. First, your payment does not change. Prepaying a conventional mortgage shortens the term; it does not lower the monthly obligation, and if cash flow is the problem then prepayment is the wrong tool. Second, timing dominates size. A lump sum in year two has more remaining months to work on than the same lump in year twenty, so the earlier prepayment saves substantially more even though the dollars are identical.
How the two schedules are built and compared
The baseline comes first. From your current balance B, monthly rate r and remaining months n, the scheduled payment is M = B·r / (1 − (1 + r)−n) — the same identity the amortization schedule calculator uses. Running that forward for n months gives the interest you are currently committed to.
The accelerated schedule uses the identical M but adds your extra in the months you specify: every month for the recurring amount, every twelfth payment for the annual amount, and once at the payment number you choose for the lump sum. Each month the recurrence is Bk = Bk−1(1 + r) − (M + Ek), and the loan is repaid the first time that reaches zero. The final payment is trimmed to exactly clear the balance rather than overshooting.
With a constant monthly extra and no lump sum, you do not need the loop. Setting Bk = 0 and solving gives a closed form: payoff = ⌈ −ln(1 − r·B / (M + E)) / ln(1 + r) ⌉. Notice the condition hiding inside it — the logarithm is only defined while M + E exceeds r·B, which is the formal statement that a payment smaller than the accrued interest never repays anything.
The saving is then simply the difference between the two interest totals. The last output divides that saving by the extra principal you actually paid, which puts prepayment on the same footing as any other use of the money.
Worked example: $300,000 at 6.5%, 30 years left, $200 a month extra
Work the default case through by hand.
- Monthly rate. r = 6.5 ÷ 1,200 = 0.005416667, and ln(1 + r) = 0.0054020.
- Scheduled payment. The payment factor at 6.5% over 360 months is 0.00632068 per dollar, so M = 300,000 × 0.00632068 = $1,896.20.
- Baseline interest. 360 × 1,896.204 − 300,000 = $382,633.
- Accelerated payment. M + E = 1,896.204 + 200 = $2,096.20.
- Payoff month. r·B = 0.005416667 × 300,000 = 1,625. Then 1,625 ÷ 2,096.204 = 0.775212, so 1 − that = 0.224788. ln(0.224788) = −1.492598, and −(−1.492598) ÷ 0.0054020 = 276.30, which rounds up to 277 payments.
- Time saved. 360 − 277 = 83 payments, six years and eleven months.
- Accelerated interest. 276 full payments of $2,096.204 is $578,552, and the 277th is trimmed to $632.35, so $579,185 leaves the account in total. Less the $300,000 of principal, interest is $279,185.
- Saving. 382,633 − 279,185 = $103,449 of interest avoided, for 276 × $200 = $55,200 of extra principal. That is $1.87 of interest saved per dollar of extra principal.
The last line is the one to carry away. At 6.5% over a full thirty-year horizon, prepayment returns considerably more than the headline rate suggests — not because the rate is higher than 6.5%, but because you are earning it for a very long time.
How to read the result, and when not to prepay
Read the interest-saved-per-dollar figure before the headline saving. It is the closest thing to a return on the money, and it lets you compare prepayment against the alternatives on equal terms. The comparison that usually decides the matter is simple: prepaying a mortgage earns you the mortgage rate, risk-free and tax-free at the margin. Any debt you hold at a higher rate should be cleared first — which for most households means credit cards, and the debt avalanche calculator puts that ordering on a formal footing.
Three situations where prepaying is the wrong move, and none of them is about arithmetic. If you have no emergency fund, money in the mortgage is money you cannot reach without a refinance or a home-equity line — home equity is the least liquid asset most families own. If your employer matches retirement contributions, the match is an immediate return that no mortgage rate approaches. And if you carry a mortgage below about 4%, the case for prepaying over almost any other use of the money is weak.
Watch what happens to the time saved as you raise the extra amount. The relationship is strongly diminishing: on the reference table below, the first $100 a month buys 48 payments and the next $100 buys only 35 more, because each additional dollar arrives on a loan that is already being retired faster. Doubling the extra never halves the term.
Finally, a mechanical point. Prepaying does not lower next month's obligation. If your goal is a smaller payment rather than a shorter loan, you want either a refinance or a recast — a recast keeps your rate and term but re-amortises the reduced balance, and many servicers offer it for a few hundred dollars after a lump-sum prepayment.
Effect of extra principal on a $300,000 loan at 6.5% with 30 years to run
| Extra per month | Payments to payoff | Payments saved | Interest saved |
|---|---|---|---|
| $0 | 360 | 0 | $0 |
| $50 | 334 | 26 | $33,582 |
| $100 | 312 | 48 | $60,995 |
| $200 | 277 | 83 | $103,449 |
| $300 | 250 | 110 | $135,115 |
| $500 | 210 | 150 | $179,759 |
| $1,000 | 153 | 207 | $241,162 |
Payments saved rises with the extra amount but by shrinking increments: $50 buys 26, the second $50 buys 22 more, and the step from $500 to $1,000 — ten times the first row's extra — buys only 57 further payments.
Mistakes that cost people the saving
- Not labelling the payment as principal. Servicers routinely hold unlabelled extra money as a prepaid future instalment, which earns you nothing. Use the principal-only field in the payment portal, or write the instruction on the cheque, then check the next statement shows the balance reduced.
- Prepaying while carrying card debt. A dollar against a 6.5% mortgage avoids 6.5% a year; the same dollar against a 24% card avoids 24%. Order matters far more than effort here.
- Paying a biweekly conversion service. The saving from a biweekly plan comes entirely from the thirteenth monthly payment it produces each year, which you can replicate for free by dividing your payment by twelve and adding that to each month. A fee for the service is a fee for arithmetic you can do yourself.
- Emptying the emergency fund. Money paid into a mortgage cannot be withdrawn. Households that prepay to zero reserves often refinance the next emergency back onto a credit card at four times the rate.
- Assuming the payment will fall. It will not. Only a recast or a refinance changes the required monthly amount.
- Ignoring the tax position. If you itemise and deduct mortgage interest, the effective rate you avoid is the note rate less your marginal rate — though since the 2017 standard-deduction increase most filers do not itemise and the point is moot for them.
Prepayment against the alternatives
Prepaying is one of four ways to reduce lifetime interest, and they are not interchangeable. Refinancing lowers the rate on the whole balance at once but carries closing costs that need recovering; the refinance break-even calculator prices that trade. Shortening the term at origination achieves the same outcome as heavy prepayment but locks you into the higher payment. Recasting keeps the rate and term but re-amortises a reduced balance, lowering the payment without a new loan. And investing instead substitutes an uncertain higher return for a certain lower one.
There is no prepayment penalty on the great majority of US mortgages written today. Regulation Z restricts prepayment penalties on qualified mortgages sharply — they are limited to the first three years, capped in size, and prohibited entirely on adjustable-rate qualified mortgages. Check your note anyway if it predates 2014 or is a non-qualified product.
One consideration that has nothing to do with rates: prepaying converts liquid savings into home equity, and equity is only realised by selling or by borrowing against the house. Households approaching a job change, a move or a period of variable income are usually better served by holding the cash, even at a lower nominal return. If you are still choosing between buying and renting at all, the rent vs buy calculator is the prior question.