Trust & transparency
Our methodology
A finance tool should show its work. Here's exactly how every calculation on Paysaurius is computed, what we assume, and where the limits are.
Amortization (the foundation)
Every strategy is built on a standard fixed-rate amortization schedule. The monthly payment is:
M = P · r / (1 − (1 + r)−n)
where P is the principal balance, r is the monthly interest rate
(annual rate ÷ 12), and n is the number of monthly payments remaining. We build the
schedule month by month: each month's interest is balance × r, the rest of the payment
reduces principal, and any extra payment is applied directly to principal. The final payment is
trimmed so the balance lands exactly at zero. When the rate is 0%, we fall back to straight-line
payments (P ÷ n).
Extra principal payments
We add your recurring monthly extra and/or one-time lump sum to principal and re-run the schedule. Your scheduled payment is unchanged, so the loan simply ends sooner. We report the new payoff month, months saved versus the baseline, and total interest saved.
Recast
We subtract your lump sum from the current balance and re-amortize the new balance over the same remaining term, at the same rate. This lowers the monthly payment while keeping the payoff date. We report the new payment, the monthly cash flow freed up, the recast fee, and interest saved versus the baseline. A recast does not shorten your term.
Refinance
We create a new loan equal to your current balance (minus any optional lump sum) at the new rate over the new term, and compute its payment and lifetime interest. The breakeven month is closing costs ÷ (old payment − new payment), when that difference is positive. Lifetime cost includes closing costs, so a lower monthly payment on a longer term can still raise total interest — we surface that explicitly.
Invest instead
Prepaying earns a guaranteed return equal to your mortgage rate. To compare investing, we grow your lump sum at an after-tax expected return — the expected return reduced by your marginal tax rate — compounded monthly over the payoff horizon. We then compare that projected gain to the guaranteed interest saved by prepaying, and we solve for the breakeven after-tax return: the rate at which investing and prepaying tie. We never present projected market returns as guaranteed.
The Decision Engine ranking
The Decision Engine runs all four strategies plus the baseline and ranks them by projected net worth at a common horizon (the baseline payoff date) — not simply by interest saved, which would always favor prepaying. To compare fairly, every path is given the same resources: the same lump sum today and the same total monthly budget (your baseline payment plus any extra). Whatever a strategy does not send to the mortgage is invested at your after-tax expected return. Net worth at the horizon is the invested side-fund minus any remaining mortgage balance. This is why a low mortgage rate with high expected returns can make investing win, while a high rate makes prepaying or refinancing win. Because money is not the only consideration, we always list non-financial caveats — emergency funds, higher-interest debt, liquidity, and risk tolerance — and frame the ranking as "based purely on these numbers."
Rounding and precision
Internal math is carried at full floating-point precision; we round only for display. Currency is shown to the dollar for large totals and to the cent for monthly payments. Our core formulas are unit-tested to the cent against hand-computed values (for example, a $300,000 loan at 6.5% over 30 years yields a $1,896.20 monthly payment).
Assumptions and limitations
- Rates are nominal annual, compounded monthly, and held constant.
- We exclude property taxes, homeowners insurance, PMI, HOA dues, and escrow.
- We exclude most lender-specific fees beyond the recast fee and refinance closing costs you enter.
- The investing comparison uses a simplified flat after-tax adjustment, not a full tax projection.
- Inputs are clamped to sensible ranges to prevent unrealistic results.
These simplifications keep the tools fast and transparent, but they mean results are estimates. Always confirm figures with your lender. See our disclaimer.