Retirement Calculator

Every projection this calculator makes rests on two pieces of compound-interest algebra. A lump sum you already hold grows to PV × (1 + i)^n, and a stream of level monthly contributions grows to the future value of an ordinary annuity: FV = PMT × ((1 + i)^n − 1) / i, where PMT is the monthly deposit, i is the annual rate divided by 12, and n is the number of months. The two results are simply added together. Work one example by hand to see the scale involved. Contribute $500 per month for 30 years at a 7% nominal annual return. Then i = 0.07 / 12 ≈ 0.0058333 and n = 360. The growth factor (1.0058333)^360 ≈ 8.1165, so FV ≈ 500 × (8.1165 − 1) / 0.0058333 ≈ $609,985. You only deposited 500 × 360 = $180,000; the remaining $429,985 — about 70% of the final balance — is compound growth on money you set aside earlier. Now start ten years later with everything else unchanged. With n = 240, (1.0058333)^240 ≈ 4.0387 and FV ≈ 500 × 3.0387 / 0.0058333 ≈ $260,463 — less than half the 30-year result, even though you still contributed two-thirds as much money. The final decade of compounding does the heaviest lifting, which is why delay is so expensive. One subtlety: this formula assumes end-of-month deposits; contributing at the start of each month (an annuity due) multiplies the result by (1 + i), a difference of about 0.58% here.

const PMT = 500;         // monthly contribution
const i = 0.07 / 12;     // ≈ 0.0058333 monthly rate
const fv = (n) => PMT * ((1 + i) ** n - 1) / i;

fv(360); // ≈ 609,985  (30 years, $180,000 deposited)
fv(240); // ≈ 260,463  (20 years, $120,000 deposited)
// starting 10 years later costs ≈ $349,522 of final balance

Accumulation is only half the problem; the other half is how much you can spend without outliving the money. The best-known answer comes from the Trinity study (Cooley, Hubbard, and Walz, 1998), which tested historical U.S. market data and found that withdrawing 4% of the portfolio in the first year of retirement, then adjusting that dollar amount for inflation each year, survived roughly 95% or more of all historical 30-year retirement periods when the portfolio held 50–75% stocks. Inverting the rule gives the popular savings target: a portfolio of about 25 times your planned annual spending. Someone who needs $40,000 per year from investments would aim for 40,000 × 25 = $1,000,000. Treat that number as an anchor, not a guarantee. The study used past U.S. returns, a 30-year horizon, and ignored fees and taxes. More recent research — Morningstar's annual State of Retirement Income reports, for example — has suggested starting rates closer to 3.3–3.8% when expected returns are lower, fees are included, or the horizon is longer. An early retiree planning for 45 or 50 years should be especially cautious: at a 3.5% starting rate the target multiple rises to about 28.6 times spending, or roughly $1,142,857 for that same $40,000 budget. The gap between 25× and 28.6× is the price of an extra margin of safety.

A subtle danger hides inside the phrase "average return." While you are only accumulating, the order of yearly returns does not matter: multiplication is commutative, so −20% followed by +30% ends at exactly the same place as +30% followed by −20%. The moment you begin withdrawing, that symmetry breaks, because each withdrawal permanently removes shares that can never participate in the recovery. Follow the arithmetic. Two retirees each start with $1,000,000 and withdraw $40,000 at the beginning of every year. Retiree A hits a bear market immediately: (1,000,000 − 40,000) × 0.80 = $768,000 after year one, then (768,000 − 40,000) × 0.90 = $655,200 after year two. The unchanged $40,000 withdrawal is now 6.1% of the portfolio, so even a strong recovery has far less capital to work with. Retiree B experiences identical returns in reverse — good years first, the crash later — so the losses land on a larger base after years of smaller-percentage withdrawals. Historical simulations show the unlucky ordering can exhaust a portfolio a decade or more sooner despite an identical average return. Standard mitigations attack the forced-selling problem directly: keep a cash or short-term bond buffer covering one to three years of spending; use flexible "guardrail" rules that trim withdrawals after bad years; or hold a temporarily higher bond allocation around the retirement date (a "bond tent") that glides back into stocks over the first decade.

The single most common planning error is admiring a large nominal projection that inflation will quietly hollow out. A $1,000,000 balance 30 years from now is not $1,000,000 of today's spending power: at 3% average inflation the deflator is 1.03^30 ≈ 2.4273, so the real value is about 1,000,000 / 2.4273 ≈ $412,000. If your plan needs a million of today's dollars, the nominal target is actually about $2.43 million. The clean fix is to run the whole projection in real terms. Convert your expected return with the Fisher equation: r_real = (1 + r_nominal) / (1 + inflation) − 1. At 7% nominal and 3% inflation that gives 1.07 / 1.03 − 1 ≈ 3.88% — noticeably less than the 4% you would get by naive subtraction, and the gap widens as inflation rises. Feed the real rate into the same annuity formula and every output is automatically expressed in today's money, which you can compare directly against today's rent, groceries, and health-care costs. For diversified global equity portfolios, long-run real returns of roughly 4–5% per year are a common educational assumption; using 6–7% real is optimistic, and double-digit assumptions almost always signal a spreadsheet error waiting to happen. Whichever rate you pick, remember that contributions should also grow with your income over time, which real-terms models handle naturally.

const nominal = 0.07, inflation = 0.03;
const real = (1 + nominal) / (1 + inflation) - 1; // ≈ 0.0388 → 3.88%

// purchasing power of $1,000,000 received in 30 years:
1000000 / 1.03 ** 30; // ≈ 412,000 in today's dollars

// nominal target that preserves $1M of today's spending power:
1000000 * 1.03 ** 30; // ≈ 2,427,262

For most people the savings rate dwarfs every other input. The reason is a double effect: saving a larger share of income both grows the portfolio faster and shrinks the annual spending the portfolio must eventually replace. Under standard educational assumptions — a 5% real return and a 4% withdrawal target — someone saving 10% of income needs about 51 years of work, while someone saving 50% needs only about 17. No realistic improvement in investment returns can close a gap that large; the savings rate can. Fees deserve the same respect. Paying 1% per year in fund and advisory costs turns a 7% return into 6%, and over a 40-year stream of steady contributions that reduces the final balance by roughly 22% — closer to a third for money invested early — because the fee compounds against you exactly as returns compound for you. The recurring mistakes are worth naming: planning in nominal dollars; assuming 10%+ annual returns because a recent decade delivered them; ignoring health-care costs and the possibility of a 30+ year retirement; and forgetting that state or occupational pensions replace part of the target, so the portfolio only needs to fund the gap. Tax treatment of retirement accounts differs enormously between jurisdictions and account types, so consult a qualified tax or financial professional about your own situation. Finally, keep the output in perspective: this calculator and this guide are educational content only, not financial advice, and real markets deliver volatile, unpredictable returns rather than the smooth average a formula assumes.

Years to retirement at 5% real return, 4% withdrawal target.
Save fraction S of income, spend (1 - S); need 25 x (1 - S).
Solve: S x ((1.05^n - 1) / 0.05) = 25 x (1 - S)

S = 10%:  1.05^n = 12.25  ->  n = ln(12.25)/ln(1.05) ~ 51 years
S = 50%:  1.05^n = 2.25   ->  n = ln(2.25)/ln(1.05)  ~ 17 years