Monthly growth factor
m = (1 + annual return)^(1/12)The effective annual return is converted into a geometrically consistent monthly factor.
Compound Interest · Methodology
How the calculation works
Illustrate how an initial investment and regular contributions could grow when returns are reinvested over time.
Return to calculatorIncluded
- An initial investment
- Month-end contributions
- Annual contribution increases
- A constant effective annual return
- Nominal and inflation-adjusted values
- Annual and cumulative compounding crossover points
Outside this method
- Investment fees and tax
- Volatility, losses and sequence risk
- Product or asset recommendations
- Withdrawals and contribution limits
- A forecast or probability range
Calculation
Core formulas
Month-end balance
Bₘ = Bₘ₋₁ × m + contributionₘGrowth is applied first and the contribution is added at month end.
Growing contribution
Cᵧ = monthly contribution × (1 + contribution growth)^(y−1)The monthly amount steps up once at the beginning of each modelled year.
Today-money value
Real value = nominal value ÷ (1 + inflation)^yearsThe final future-pound balance is converted into estimated current purchasing power.
Annual crossover
Annual growth > contributions made during that yearThis identifies when modelled compounding first adds more in one year than the investor adds during that year.
Timing convention
When cash flows occur
The initial investment is present at the start. The effective annual return compounds monthly, contributions enter at each month end and the monthly contribution changes once a year when contribution growth is above zero.
Limitations
What the result cannot establish
- A constant return hides volatility and the order in which real gains and losses occur.
- The return is before fees and tax, both of which can materially reduce the outcome.
- General inflation may not match a household’s own spending pattern.
- The annual crossover is sensitive to contribution increases as well as returns.
- Rounding displayed values to whole pounds can create small differences from the underlying calculation.
Reference tests
Numerical checks
| Case | Inputs | Expected result |
|---|---|---|
| Lump-sum compounding | £10,000 initial; £0 monthly; 5% return; 10 years | £16,288.95 future value |
| Month-end contributions | £0 initial; £100 monthly; 5% effective return; 1 year | £1,227.26 future value |
| Zero return | £5,000 initial; £100 monthly; 10 years; 0% return | £17,000 balance and £0 growth |
Evidence