How this instrument works
Interest saved, % of original answers one question: what share of the interest a mortgage would otherwise cost disappears if a fixed extra amount goes toward principal every month, starting now and continuing for the life of the loan. Expressing the effect as a percentage rather than a raw dollar figure is what makes the number portable — a $119,702 dollar saving means little without knowing the size of the loan it came from, but 34.4% means the same thing whether the loan is $150,000 or $600,000, which is why comparing extra-payment plans across two different mortgages calls for this ratio rather than the dollar total.
The base interest, baseTotalInterest, comes from straightforward arithmetic: the standard monthly payment, priced from the ordinary amortization formula, times the number of payments in the term, minus the loan itself — whatever is left over is the total lifetime interest. The accelerated figure, newTotalInterest, cannot be found the same way, because adding a flat extra amount to the payment does not change any single row of the payment table — it changes how many rows there are. Solving for that new, shorter payoff time means inverting the annuity formula for time rather than for payment, which is why a natural logarithm shows up where the payment formula has none. A common misreading treats the saved share as proportional to the extra amount — doubling a $300 monthly extra to $600 lifts the saved share from roughly 34% to roughly 50%, not to 69%, because later extra dollars chip away at an already-smaller remaining balance.
The model assumes the extra amount is committed for the full remaining life of the loan, applied to principal every month with no prepayment penalty, no missed payment, and no change in rate. It does not represent a one-time lump sum, a raise that lets the extra amount grow over time, or a household that skips a few months in a lean year — any of those change the real payoff path enough that the reported percentage becomes an upper bound rather than a guarantee. It also leaves out property tax, insurance, and any opportunity cost of the money committed — whether those dollars would do more against a higher-rate debt elsewhere is a separate question this instrument does not answer.
- Enter the amount borrowed in Loan amount, $ and the lender's quoted rate in Annual interest rate, %.
- Set the original repayment schedule in Loan term, years.
- Enter the flat amount to add every month in Extra payment, $/month — set it to $0 to see the unmodified schedule.
- Compare Total interest, original schedule against Total interest, with extra payments to see the dollar effect.
- Read Interest saved, % of original for the share of lifetime interest the extra payment removes.
Worked example — $300 a month on a $300,000 loan
Borrow $300,000 at 6% over a 30-year term and the standard schedule — 360 payments of $1,798.65 — racks up $347,514.57 in interest over the life of the loan, more than the original principal itself. That figure is baseTotalInterest, reported before any extra payment is considered.
Add $300 a month on top of that payment and the loan is solved for a new, shorter payoff time instead of a new payment size: interest drops to $227,812.50 (newTotalInterest), a reduction of $119,702.07 that works out to 34.4452% of the original interest bill (interestSavedPercent) — roughly a third of everything this loan would have cost in interest disappears for an extra $300 committed every month.
Questions
Why is the savings shown as a percentage instead of a dollar amount?
Because a dollar figure only means something next to the loan it came from. Saving $119,702 sounds dramatic on a $300,000 loan and unremarkable on a $2 million one, but 34.4% of the original interest bill describes the same relative effect on either loan, which is what makes the percentage useful for comparing extra-payment plans across mortgages of different sizes.
Does doubling the extra payment double the interest saved?
No. Raising the extra payment from $300 to $600 a month on the example above lifts the saved share from about 34.4% to about 50.5%, not to roughly 69%. Each additional dollar of extra payment is applied against an already-smaller remaining balance, so later dollars remove less lifetime interest than earlier ones — the relationship is concave, not linear.
How is the new payoff time calculated, since the payment just gets bigger?
By inverting the ordinary amortization formula. Instead of solving for a payment given a fixed number of months, the instrument fixes the new payment — standard payment plus the extra amount — and solves for how many months that payment needs to reach zero balance, a step that requires a natural logarithm rather than the simple algebra used to find the payment itself.
Is this the same idea as a biweekly mortgage payment?
No. A biweekly schedule squeezes the existing payment onto a 26-payment-a-year calendar and gains one extra monthly-equivalent payment automatically, without raising the per-payment amount. This instrument instead adds a separately chosen, genuinely larger amount to every monthly payment — a voluntary top-up, not a calendar trick — so the two produce different payoff times even at similar-looking extra amounts.
What happens if I stop the extra payment partway through the loan?
The reported percentage assumes the extra amount continues every month for the entire new, shorter term — stopping early leaves the loan on a schedule between the original and the accelerated one, with less interest saved than shown here. Recalculate with the remaining balance and remaining term as new inputs to see the effect of resuming, changing, or stopping the extra amount partway through.
Does the calculation include property tax, insurance, or lender fees?
No. It works only with principal, rate, term and the extra payment, and reports interest on that basis alone. Escrowed items such as property tax, homeowner's insurance and mortgage insurance are billed separately by most lenders and do not affect how the interest portion of a principal-and-interest payment is computed here.
References
- Consumer Financial Protection Bureau — Loan options and amortization
- Federal Reserve — Consumer's guide to mortgage settlement costs
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.