Contractual mortgage payment
Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]The starting balance, monthly mortgage rate and remaining months determine the normal repayment.
Mortgage Overpayment vs Invest · Methodology
How the calculation works
Compare mortgage overpayment, investing and a user-selected split using the same starting cash and the same original mortgage-term horizon.
Return to calculatorIncluded
- A standard capital-and-interest repayment mortgage
- One-off and regular spare cash
- A user-entered overpayment charge
- Overpay, invest and split strategies
- Low, central and high investment-return scenarios
- Fees and simplified wrapper adjustments
- Cash-flow recycling after early mortgage repayment
- A solved break-even investment return
Outside this method
- Interest-only, offset and flexible mortgages
- Changing mortgage rates and future product pricing
- Lender-specific daily interest and overpayment limits
- Exact Income Tax or Capital Gains Tax
- Investment return probabilities or sequence risk
- Advice about suitability, products or asset allocation
Calculation
Core formulas
Mortgage balance
Bₘ = Bₘ₋₁ + interestₘ − normal payment − overpaymentₘOverpayments reduce the balance while the normal payment stays unchanged, so the modelled term shortens.
Investment balance
Iₘ = Iₘ₋₁ × net monthly factor + contributionₘThe gross return is reduced by the entered annual fee and, for a general account, the user’s annual tax-drag estimate.
Net mortgage-interest saving
Baseline interest − strategy interest − entered overpayment chargeThis separates contractual interest avoided from any charge consumed by the overpayment decision.
Fair end-value comparison
End value = investment value after wrapper adjustments at original mortgage endOnce a strategy repays the mortgage early, the released normal payment and extra cash are invested for the remaining months.
Break-even return
Solve Invest end value − Overpay end value = 0A bisection search finds the gross annual investment return that equalises the two strategies under the entered costs and wrapper assumptions.
Timing convention
When cash flows occur
The lump sum is allocated at the start. Mortgage interest and investment growth are applied monthly. Regular cash is allocated at month end. After the mortgage clears, the unused normal payment and full regular amount move into the investment until the original term ends.
Limitations
What the result cannot establish
- Holding the mortgage rate constant can materially overstate or understate the eventual interest saving.
- A smooth low, central or high return does not reproduce market volatility or the order of gains and losses.
- The pension multiplier and withdrawal keep-rate are user estimates, not a pension tax calculation.
- The annual tax-drag input cannot reproduce allowance use, realised gains, dividends or changing tax rates.
- Overpaying could improve a future loan-to-value band, but any resulting mortgage-rate benefit is excluded.
- The model assumes spare cash remains available and is consistently redirected after the mortgage is repaid.
Reference tests
Numerical checks
| Case | Inputs | Expected result |
|---|---|---|
| Standard mortgage payment | £250,000 balance; 4.5% rate; 25 years | Contractual payment of approximately £1,390 a month |
| Lump-sum overpayment | Same mortgage; £10,000 immediate overpayment; normal payment unchanged | Approximately £19,584 gross interest saved and repayment around 21 months earlier |
| No spare cash | £0 lump sum and £0 monthly amount | No allocation comparison is produced |
Evidence