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Mortgage Refinance Formulas and Calculations

Learn the refinance payment and amortization formulas, break-even calculation, closing-cost treatment, horizon comparison, and a checked worked example.

How do the Refinance Calculator formulas work?

This formula page defines the variables used by the Refinance Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Refinance Formula Overview

The calculator builds two fixed-rate amortization schedules: one for the remaining current mortgage and one for the proposed replacement loan. It compares their payments, monthly interest, principal, balances and total interest, then includes entered closing costs in the break-even, horizon and lifetime views.

M=Pi1−(1+i)−nM=P\frac{i}{1-(1+i)^{-n}}

The payment equation is evaluated independently for each loan. It models principal and interest only; ownership costs are handled outside this engine.

Variable Definitions

SymbolMeaningUnit or convention
BCurrent unpaid principal balanceCurrency
PPrincipal for the schedule being calculatedCurrency
MScheduled monthly principal-and-interest paymentCurrency per month
rAnnual fixed note ratePercentage, such as 6.5
iMonthly interest rater / 1,200
nScheduled monthly paymentsYears x 12 + months
CEntered closing costsCurrency
CoutEntered cash-out proceedsCurrency
hComparison horizonYears x 12 months
BtBalance after payment tCurrency
ItInterest in payment period tCurrency
QtPrincipal paid in payment period tCurrency

Monthly Payment

The proposed principal is calculated before the payment formula:

Pnew=B+Cout+CfinancedP_{new}=B+C_{out}+C_{financed}

Cfinanced equals entered closing costs when the financing option is selected and zero otherwise. The current principal is simply the entered current balance.

For a positive monthly rate, both payments use:

i=r1200i=\frac{r}{1200}
M=Pi(1+i)n(1+i)n−1=Pi1−(1+i)−nM=P\frac{i(1+i)^n}{(1+i)^n-1}=P\frac{i}{1-(1+i)^{-n}}

When the annual rate is exactly 0%, the engine avoids division by zero and uses M = P / n.

Amortization

Each schedule starts with B0 = P. For month t:

It=Bt−1iI_t=B_{t-1}i
Qt=min⁡(Bt−1,max⁡(0,M−It))Q_t=\min(B_{t-1},\max(0,M-I_t))
Bt=max⁡(0,Bt−1−Qt)B_t=\max(0,B_{t-1}-Q_t)

The annual comparison sums the monthly interest and principal rows for each calendar-sized loan year and uses the last row as the year-end balance. The final principal amount is capped so a schedule cannot end below zero.

Payment savings and break-even

S=Mcurrent−MnewS=M_{current}-M_{new}
NBE=⌈CS⌉N_{BE}=\left\lceil\frac{C}{S}\right\rceil

The break-even month is calculated only when S is positive. If costs are zero and savings are positive, break-even is month 0. If the proposed payment is equal or higher, no simple payment break-even is reported.

Horizon and lifetime comparisons

Savingsh=∑t=1hIcurrent,t−∑t=1hInew,t−CSavings_h=\sum_{t=1}^{h}I_{current,t}-\sum_{t=1}^{h}I_{new,t}-C
Lifetime savings=Icurrent,total−(Inew,total+C)Lifetime\ savings=I_{current,total}-(I_{new,total}+C)

The horizon view also reports both remaining balances. A positive value means lower modeled borrowing cost under the proposed loan; a negative value means higher cost.

Extra Payments

The refinance engine intentionally uses scheduled payments without extra principal so the current and proposed contract terms are compared consistently. Extra payments change future interest and payoff time, so mixing an accelerated current schedule with a minimum-payment proposed schedule would distort the result.

To model the effect, first calculate the refinance comparison without extras. Then run the same extra-principal strategy for each loan in the Extra Payment Calculator. In a schedule with extra principal Et, the conceptual balance becomes:

Bt=max⁡(0,Bt−1−Qt−Et)B_t=\max(0,B_{t-1}-Q_t-E_t)

This equation explains why earlier principal reduction lowers later interest, but Et is not applied inside the refinance result.

Ownership Costs

Property tax, homeowners insurance, HOA dues, maintenance and utilities are excluded from the refinance payment formula. They belong to the property rather than the principal-and-interest schedule and often continue after refinancing.

Mortgage insurance, escrow requirements and prepaid amounts can change between offers. Compare those lender disclosures separately. For a full housing-payment scenario, add the relevant amounts in the Mortgage Payment Calculator.

Worked Calculation

Use a $300,000 current balance, 6.5% current rate, 25 years remaining, 5.5% proposed rate, 25-year new term, $6,000 in upfront costs, no cash out and a five-year horizon.

  1. Current monthly rate: 6.5 / 1,200 = 0.005416667.
  2. Proposed monthly rate: 5.5 / 1,200 = 0.004583333.
  3. Both schedules contain 25 x 12 = 300 months.
  4. Current payment: $2,025.62.
  5. Proposed payment: $1,842.26.
  6. Monthly savings: $2,025.62 - $1,842.26 = $183.36.
  7. Break-even: ceil($6,000 / $183.36) = 33 months.
  8. Five-year current interest is $93,223.78; proposed interest is $78,350.32.
  9. Five-year net savings: $93,223.78 - $78,350.32 - $6,000 = $8,873.45.
  10. Estimated lifetime savings are $49,007.70.

Displayed money is rounded to cents. The engine uses the full calculated values when producing the amortization rows and comparisons.

Assumptions

  • Both mortgages are fixed-rate, fully amortizing loans paid monthly.
  • Rates remain unchanged and every scheduled payment is made on time.
  • Closing costs are entered as one nonnegative total and counted once in cost comparisons.
  • Cash out is borrowed principal, not savings or a borrowing cost; interest on it is included.
  • Taxes, insurance, mortgage insurance, escrow changes, points, lender credits, penalties, tax effects and opportunity cost are outside the formula unless reflected in entered closing costs.
  • The comparison horizon is limited to the available months in the two schedules.

Formula FAQ

Why is break-even rounded up?

Costs are not fully recovered until accumulated savings reach the full entered amount. A fractional month therefore moves to the next complete payment month. Use realistic inputs and review the Refinance Calculator formula assumptions before relying on this result for decisions.

Why can break-even be unavailable?

The formula requires positive monthly savings. A shorter term may raise the payment while still lowering lifetime interest, so break-even is not the appropriate measure for that scenario. Review the Refinance Calculator formula assumptions before relying on this result for decisions.

Why are balances shown with horizon savings?

Payment and interest do not show how much principal remains. Comparing balances at the same future date reveals differences in equity progress. For a useful Refinance Calculator formula result, use realistic inputs, compare relevant scenarios, and review the stated assumptions before making a decision.

Are financed closing costs counted twice?

No. They are added to proposed principal, so they affect payment and interest, and the entered cost is included once in the borrowing-cost comparison. Use realistic inputs and review the Refinance Calculator formula assumptions before relying on this result for decisions.

References

Use the Refinance Calculator