Understanding retirement maths
The pot, and what it has to last for.
Two compounding curves, an inflation tax, and the rule of thumb that finance professors spend their careers arguing about.
Two phases, one curve each.
Every retirement model has the same shape. In the accumulation phase, you contribute regularly to an investment pot that compounds at some assumed real return. In the drawdown phase, you withdraw from that pot at some rate, while it continues to compound on what's left. The retirement number — the figure you're trying to hit — is the size of the pot at the transition between the two phases, big enough that the drawdown phase doesn't deplete it during the time you'll need it.
The future-value formula.
The pot after N years of monthly contributions C, starting from P, growing at annual rate r (split into monthly r/12), is the standard ordinary-annuity future value: present value compounded plus each contribution compounded from when it was made. The closed form is one line, but the takeaway is that the curve is exponential in time and linear in contribution — every extra year you can leave it untouched matters more than every extra pound you can find to add.
FV = P(1+r/12)ⁿ + C · [(1+r/12)ⁿ − 1] · (12/r)
Nominal vs real returns.
The most common modelling mistake is mixing nominal and real numbers. A nominal 8 % return with 3 % inflation is a 5 % real return — what your pot can actually buy in today's money grows at the real rate. Either work entirely in nominal currency (and inflate your target spending too) or entirely in real (and let inflation drop out). The worst middle ground is contributing in today's money, projecting at a nominal return, and judging the result against a target priced in today's pounds. That mistake tends to flatter the number by 30–60 % over a 30-year horizon.
The 4 % rule, and what it actually says.
The 4 % rule is the most-cited rule of thumb for the drawdown phase. It comes from William Bengen's 1994 paper studying 50-year-old retirees with a 60/40 stock/bond portfolio across every 30-year window in US market history from 1926. He found that an initial 4 % withdrawal, adjusted annually for inflation, survived every historical window. The rule has limits — it assumes US market returns, 30-year horizons, a specific asset mix and constant real spending — but inverted, it gives you the simplest target: aim for 25 × your annual retirement spending. Want £30,000 a year in today's money? Aim for £750,000 in real terms.
target pot ≈ 25 × annual spending (in today's money)
A worked path.
A 35-year-old with £20,000 saved, contributing £500 a month, expecting 5 % real return, retiring at 65. Thirty years of monthly compounding at 5 % gives the present pot a 4.32× multiplier — £20,000 becomes £86,400. The contribution stream, by the future-value annuity formula, builds to about £416,000. Total pot at 65 ≈ £502,000 in today's money. At 4 % real drawdown, that funds ≈ £20,000 a year, indexed to inflation, for 30 years.
Pot growth — present £20,000
FV = P × (1 + 0.05/12)^(12 × 30)
Monthly compounding for 30 years at 5 % real.
£20,000 × (1.004167)^360 = £20,000 × 4.32
= £86,400
Contributions — £500/month for 30 years
FV = C × [(1 + r/12)^n − 1] × (12/r)
Each month's £500 compounds from when it was paid.
£500 × [(1.004167)^360 − 1] × (12/0.05)
= ≈ £416,000
Sensitivity — which lever matters?
Time is the biggest lever, because the curve is exponential. Doubling your monthly contribution doubles the contribution part of the pot; doubling your saving horizon roughly quadruples it. Return matters next — one percentage point of real return added across 30 years inflates the pot by 30–35 %. Inflation eats from the other end: a 1 % higher inflation assumption shaves a comparable bite off the target's real value. Order of decisions: start sooner, choose a portfolio that earns the real return you need, contribute as much as you can sustain — in that priority.
Sequence-of-returns risk.
The accumulation maths is symmetric: a bad year early and a good year late produces the same end-pot as a good year early and a bad year late. The drawdown maths is not. Big losses in the first decade of retirement, while withdrawals are coming out at the original real-pound rate, can permanently impair the pot — you sell at the bottom to fund spending, then have less invested for the recovery. Almost all "safe withdrawal rate" research is really about surviving the worst historical opening decades. Plans that ignore sequence risk (assume constant returns) systematically overstate how much you can spend.
What this calculator is for.
A retirement calculator is a useful sketch, not a financial plan. It tells you whether your current path is in the right order of magnitude, where the levers are, and what changing one of them does. It does not model tax bands, state pensions, employer matching nuances, asset-allocation glide paths, healthcare costs in retirement, or the right-tail risk of needing care at 85. Use the figure here to start the conversation; use a regulated adviser to settle it.