Investment after fees
Vₜ = V₀ × [(1 + return) × (1 − fee)]ᵗReturn and the annual percentage fee are combined multiplicatively once in each modelled year.
Assumptions Lab · Methodology
How the calculation works
Show how strongly a long-horizon illustration depends on returns, fees, inflation, earnings growth and property-price change.
Return to calculatorIncluded
- Separate starting values for an investment, a property and annual income
- Future-pound and today-money values
- A common real-value index for unlike starting amounts
- The purchasing power of £100,000 cash without interest
- A one-percentage-point sensitivity test for every entered rate
Outside this method
- A forecast, probability or historical range
- Investment contributions, mortgage debt, tax and spending
- Asset-allocation, product or property recommendations
- Cash interest and investment volatility
- A combined net-worth or affordability result
Calculation
Core formulas
Income or property value
Vₜ = V₀ × (1 + annual change)ᵗThe entered growth rate stays constant throughout the selected horizon.
Today-money value
Real value = future value ÷ (1 + inflation)ᵗThis converts a future-pound amount into estimated present purchasing power.
Common index
Indexₜ = 100 × real valueₜ ÷ starting valueEach line starts at 100 so its change in purchasing power can be compared without adding unlike amounts.
Timing convention
When cash flows occur
All annual assumptions compound once per modelled year. The sensitivity view recalculates the relevant outcome after moving one assumption down and up by one percentage point while holding every other entry constant.
Limitations
What the result cannot establish
- Constant rates conceal volatility, sequence effects and changing economic conditions.
- Annual income is a flow while property and investment values are assets; they are deliberately shown separately.
- General inflation may not reflect a household’s own spending pattern.
- A property-price assumption says nothing about saleability, costs, maintenance or local conditions.
- The fee sensitivity is bounded at 0% when a one-point reduction would otherwise be negative.
Reference tests
Numerical checks
| Case | Inputs | Expected result |
|---|---|---|
| Investment compounding | £100,000; 5% return; 0% fee; 10 years | £162,889 in future pounds |
| Cash purchasing power | £100,000 cash; 2.5% inflation; 20 years | Approximately £61,027 in today’s money |
| Flat real property value | 2% property growth; 2% inflation | Real-value index remains at 100 |
Evidence