Last Updated: February 2026
PayoffVsInvest provides transparent, math-based financial decision tools designed to compare debt repayment versus investing using inflation-adjusted, tax-aware modeling. This page explains the formulas, assumptions, and logic used across all calculators on this site.
Core Modeling Philosophy
All calculators use consistent financial mathematics to ensure fair, apples-to-apples comparisons. We model both paths — paying down debt or investing — under identical time horizons, compounding frequencies, inflation assumptions, and tax treatment.
Results are expressed in both nominal dollars and inflation-adjusted “real dollars” to reflect true purchasing power.
1. Loan Modeling
Debt is modeled using standard fixed-rate amortization with monthly compounding. Payments are assumed to occur at the end of each period (ordinary annuity).
Payment Formula:
PMT = P × [ r(1 + r)^n ] / [ (1 + r)^n − 1 ]
Where:
- P = Loan principal
- r = Monthly interest rate
- n = Total number of payments
Any lump-sum or extra payments are applied immediately to the principal at the start of the next period, reducing interest accrued in all subsequent months.
2. Investment Growth Model
Investments are modeled using monthly compounding to match loan payment frequency. Future value is calculated using:
FV = PV × (1 + r)^n
Where:
- PV = Present value
- r = Monthly return
- n = Number of months
To convert nominal returns into real (inflation-adjusted) returns, we apply the Fisher Equation:
r_real = (1 + r_nominal) / (1 + r_inflation) − 1
This provides a more accurate real return than simple subtraction, especially during elevated inflation periods.
3. Inflation Logic
- Default inflation: 2.8% annually
- User-adjustable for custom scenarios
- Applied to both investments and debt
Inflation reduces the real value of future investment dollars while also decreasing the real cost of fixed-rate debt over time. This dual application reflects real-world purchasing power.
4. Tax Treatment
Investments
Investment returns assume long-term capital gains treatment. An effective annual tax drag is applied based on the user’s estimated marginal tax rate:
After-Tax Return = Nominal Return × (1 − Tax Rate)
Debt
Where applicable, the model incorporates:
- Mortgage Interest Deduction
- Student Loan Interest Deduction
After-tax debt rate:
After-Tax Debt Rate = Nominal Rate × (1 − (Deductible % × Marginal Tax Rate))
Eligibility depends on individual circumstances.
5. Break-Even Return
Break-even return is defined as the annual investment rate at which both strategies produce equal net worth at the end of the selected term.
Conceptually:
- Investment future value (after tax)
- equals
- Interest avoided plus compounded saved payments
Simplified hurdle approximation:
BreakEven ≈ AfterTaxDebtRate / (1 − InvestmentTaxDrag)
6. Default Assumptions
| Parameter | Default |
|---|---|
| Investment Return | 7.0% nominal annually |
| Inflation | 2.8% annually |
| Marginal Tax Rate | 22% |
| Loan Term | 30 years |
All defaults are user-adjustable.
7. Output Definitions
- Net Worth Difference: Ending assets minus liabilities across strategies.
- Effective Real Interest Rate: Debt rate adjusted for inflation and tax deductibility.
- Break-Even Return: Minimum investment return required to outperform debt payoff.
8. Data Sources
- Federal Reserve — Effective Federal Funds Rate benchmarks
- Bureau of Labor Statistics (CPI) — Consumer Price Index inflation data
- IRS Publication 936 — Home Mortgage Interest Deduction
- IRS Publication 550 — Investment Income and Expenses
Change Log
- February 2026 — Initial methodology published.
Important Notice
Calculator outputs are estimates only and not financial advice. See our Financial Disclaimer.