How It Works
- Both run to the same horizon T — the date the debt would clear on its normal schedule
- Invest: pay the normal payment, invest the extra amount every month until T
- Pay down: throw the extra at the debt until it clears early, then invest the freed-up payment plus the extra for the rest of the months to T
- Winner: whichever strategy has the larger investment pot at T
- Every month you spend the same payment + extra in both strategies — that is the fairness guarantee
Key Assumptions
- 1Expected investment returns are nominal (not inflation-adjusted) and constant — they are your estimate, not a guarantee
- 2Prepaying earns a guaranteed return equal to the debt's interest rate; investing only wins if your expected return actually holds
- 3The invest-side rate is your assets' total return: growth plus the full dividend yield, whether reinvested or paid out
- 4The debt follows its contractual schedule; the monthly payment + extra is identical under both strategies
- 5Tax and inflation are optional and applied separately (tax on nominal gains first, then inflation deflates)
Mathematical Approach
Monthly return r = Annual Total Return / 12 Invest side (A): FV_A = Extra × [((1 + r)^n − 1) / r] where n = months from now to T Pay-down side (B): nothing invested while the debt is being cleared, then FV_B = Σ (that month's baseline payment + Extra) × (1 + r)^(months left to T) Interest saved = future interest on the normal schedule − future interest on the accelerated schedule. Break-even rate: the annual return at which FV_A equals FV_B, solved numerically (on after-tax pots when the tax simulation is on). With tax on, each side is taxed on its own gains over its own contributions: tax = max(0, FV − contributions) × rate.
Important Limitations
- Prepaying is a guaranteed return; the investment return is only an expectation — market volatility is not modeled
- Mortgage-interest tax deductibility is not modeled (it can make debt cheaper than shown)
- Dividends are taxed once at exit here, not each year they are paid
- When the extra payment's currency differs from the debt's, the amount is relabelled rather than converted
- Results become less reliable over long horizons and assume the contractual schedule holds
Important: This is a decision aid, not advice. Prepaying debt guarantees you save its interest rate, while investing beats it only if your expected return actually materializes. Consider your risk tolerance and emergency savings alongside these numbers.
Frequently Asked Questions
Should I invest or pay off debt first?
Mathematically, prepaying a debt earns a guaranteed return equal to its interest rate, while investing wins only if your expected return actually materializes. Wealth Path compares both strategies with identical monthly outflows to the same end date, shows which pot is larger, and computes the break-even return where they tie.
What is the break-even rate in this comparison?
It is the annual investment return at which investing the extra and prepaying the debt end with exactly the same pot at the horizon. If your realistic expected return is below it, prepaying wins; above it, investing wins.
Why do both strategies end at the same date?
Ending both at the debt’s natural payoff date, with the same money spent each month, is the only fair comparison — otherwise one side would simply have invested more money or for longer.
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The information and calculations provided are for informational and educational purposes only and should not be considered financial, investment, or professional advice. Projections are hypothetical, based on assumptions that may not reflect actual market conditions. Past performance does not guarantee future results, and all investments carry risk of loss. Consult a qualified financial professional before making financial decisions.