Repayment payment
Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]The contractual payment amortises the opening loan over the remaining term at the entered monthly rate.
Remortgage Decision Lab · Methodology
How the calculation works
Compare two repayment remortgage deals on a matched balance, term and holding period by separating interest and net fees from capital repayment and monthly cash flow.
Return to calculatorIncluded
- Two initial interest rates and deal periods
- Follow-on rates where the comparison extends beyond an initial period
- Cash-paid or mortgage-financed product fees
- Legal, valuation and broker fees
- Cashback and incentives
- A current-deal early-repayment charge
- Monthly overpayments
- Interest, capital repaid, cash outflow and economic cost
- A cumulative-cost crossover month
- Current and exit loan-to-value
- Cash needed for the next common LTV threshold
- A one-percentage-point rate sensitivity
Outside this method
- Mortgage advice or a product recommendation
- Eligibility and affordability assessment
- Interest-only, offset, flexible and part-and-part structures
- Daily lender interest and exact payment dates
- Product-specific overpayment limits and future early-repayment-charge schedules
- Porting and further advances
- A forecast of interest rates or property value
- Opportunity cost on cash fees, cashback or LTV paydown
- Tax and insurance
Calculation
Core formulas
Financed product fee
Opening loan = mortgage balance + product feeWhen the fee is added to the loan, it also attracts modelled mortgage interest.
Monthly balance
Bₘ = Bₘ₋₁ + interestₘ − contractual payment − overpaymentThe payment is limited to the balance due and is recalculated if an entered follow-on rate starts.
Economic cost
Interest + product fee + other fees + current ERC − cashbackCapital repayment is excluded because it reduces debt rather than consuming household wealth.
Cash outflow
Monthly payments + cash-paid fees + other fees + current ERC − cashbackThis separate measure helps assess liquidity and affordability.
Cost crossover
First month where sign[cumulative cost A − cumulative cost B] reversesA crossover can show how long a higher-fee, lower-rate product takes to recover its opening cost.
Loan-to-value
LTV = mortgage balance ÷ entered property valueThe target paydown is the cash needed to reach the next lower threshold in a 95%, 90%, 85%, 80%, 75%, 70%, 65% and 60% grid.
Timing convention
When cash flows occur
Fees, cashback and the current early-repayment charge occur at the start. Interest and payments occur monthly. A product fee added to the mortgage is included in the opening loan. If a fixed period ends inside the comparison window, the contractual payment is recalculated at the follow-on rate over the remaining term.
Limitations
What the result cannot establish
- A lender may calculate interest daily and round payments differently.
- The comparison assumes both products complete at the same time and start from the same balance.
- A stated cashback or free legal service can have conditions and different cash timing.
- The property value is held constant; a lender's valuation may move the LTV and available rate band.
- The one-point stress moves all entered initial and follow-on rates mechanically and is not a tracker-path model.
- Economic cost does not value optionality, portability, advice, service quality or the opportunity cost of cash.
Reference tests
Numerical checks
| Case | Inputs | Expected result |
|---|---|---|
| Zero-rate repayment | £120,000 balance; 10-year term; 0% rate | £1,000 contractual monthly payment |
| Cash product fee | £999 fee paid in cash | £999 opening economic and cash cost before other inputs |
| Financed product fee | £200,000 balance; £999 fee added | £200,999 opening loan and interest charged on the fee |
| Cashback | £500 cashback and no fees | Opening economic cost reduced by £500 |
| LTV threshold | £330,000 balance; £400,000 value | 82.5% LTV and £10,000 needed to reach 80% |
Evidence