Mathematical Formulation
Buyer's Net Wealth at Year T
buyerNetWealth(T) = propertyValue(T) - remainingMortgageBalance(T) - sellingCosts(T)Where:
propertyValue(T) = propertyPrice × (1 + houseAppreciation)^TremainingMortgageBalance(T)calculated using standard amortisation schedulesellingCosts(T) = propertyValue(T) × sellingCostsAgent% + sellingCostsLegal
Renter's Net Wealth at Year T
renterNetWealth(T) = initialDepositInvested(T) + cumulativeMonthlyDifferentialInvested(T)Where:
initialDepositInvested(T) = (deposit + buyingCostsAvoided) × (1 + investmentReturn)^TbuyingCostsAvoided = SDLT + legalFees + surveyFees + mortgageArrangementFee
Monthly Differential Calculation
For each month m from 0 to T×12:
monthlyBuyerCost(m) = mortgagePayment + maintenance + insurance + serviceCharges(when mortgage active)monthlyRenterCost(m) = rent × (1 + rentGrowth)^(m/12)differential(m) = max(0, monthlyBuyerCost(m) - monthlyRenterCost(m))
Asymmetry Assumption
When renter's monthly cost exceeds buyer's cost, differential is set to 0. This reflects that buyers cannot notionally "save" money when their committed mortgage payments are lower than market rent — the mortgage commitment remains fixed regardless.
UK 2026 Default Values
| Parameter | Default Value | Source/Rationale |
|---|---|---|
| Property Price | £268,000 | ONS HPI Feb 2026 UK average |
| Deposit | 10% (£26,800) | UK convention for first-time buyers |
| Mortgage Rate | 5.75% | Moneyfacts avg 5-year fix April 2026 |
| Mortgage Term | 25 years | UK convention |
| Monthly Rent | £1,377 | ONS PIPR March 2026 UK average |
| Rent Growth | 3.4% p.a. | ONS PIPR YoY March 2026 |
| House Appreciation | 1.2% p.a. | ONS HPI YoY Feb 2026 |
| Investment Return | 5.0% p.a. | Conservative real-return assumption (60/40 portfolio) |
| Maintenance Rate | 1.5% of value p.a. | Midpoint of 1% rule and ~3% recent actuals |
| Time Horizon | 25 years | Match mortgage term |
Advanced Cost Assumptions
Upfront Costs
- Legal Fees: £1,500 (combined solicitor + searches)
- Survey Fees: £500 (homebuyer's report)
- Mortgage Arrangement: £1,000 (typical)
- SDLT/LBTT/LTT: Calculated per region and buyer type
Ongoing Costs
- Buildings Insurance: £30/month (UK average)
- Service Charge: £0/year (leasehold flag)
- Ground Rent: £0/year (leasehold flag)
- Estate Agent Fee: 1.5% of property value
- Legal Fees on Sale: £1,000
Regional Tax Calculations
The calculator incorporates the complete SDLT, LBTT, and LTT calculation engines to provide accurate tax calculations across all UK regions:
- England & Northern Ireland: SDLT with April 2025 rate changes, FTB relief up to £300k (properties up to £500k), 5% additional property surcharge
- Scotland: LBTT with FTB relief up to £175k, 6% additional dwelling supplement
- Wales: LTT with no FTB relief, 4% higher rates surcharge
Break-Even Calculation
The break-even year is the first year T where:
buyerNetWealth(T) ≥ renterNetWealth(T)If no such year exists within the time horizon, the calculator returns null and displays "Renting wins over the full horizon at these inputs".
Edge Cases & Validation
- Deposit > Property Price: Validation error prevents submission
- Mortgage Term Complete: After mortgage is paid off, buyer pays only maintenance/insurance/service charges
- Input Boundaries: Property price £50k–£5m with warnings, mortgage rate 1%–15% with warnings
- Leasehold Properties: Service charge > £0 prompts leasehold confirmation and explanation
- Regional Variations: Scotland/Wales selector drives correct LBTT/LTT calculations
Update History
Last updated: 8 May 2026
Initial methodology publication with UK 2026 defaults
Author & Review
Methodology developed by: Rent vs Buy Calculator Team
Last reviewed: 8 May 2026 | Reviewed by financial modelling specialists