Compound Growth Calculator

The calculator runs a year-by-year simulation. Within each year, contributions are split into the chosen number of periods (e.g., 12 for monthly) and added at the end of each period. The per-period growth rate is derived from the annual return: periodRate = (1 + annualReturn)^(1/periods) − 1. This correctly reflects that more frequent contributions spend more time compounding, producing slightly higher returns than a single annual deposit at the same rate.

In year Y, the annual contribution is: baseAnnualContrib × (1 + contribGrowthRate)^(Y − 1). This models a rising savings rate — for example, someone saving 15% of a salary that grows 4% per year effectively contributes 4% more each year. The result is a non-linear deposit curve that accelerates over time, compounding more capital into the portfolio in later years than a flat contribution schedule would. The side panel's Year 1 vs. Year N comparison makes this growth visible.

When variance is set above 0%, the chart adds an optimistic scenario (base + variance) and a pessimistic scenario (base − variance), with the region between them shaded. The band is not a confidence interval or probability range — it is a simple sensitivity test showing how much outcomes diverge if your actual return is consistently higher or lower than expected. Real returns fluctuate year to year; this tool models a constant rate, so the band helps approximate that uncertainty.

Your nominal final balance is divided by (1 + inflationRate)^years to produce the real (inflation-adjusted) value. This answers: "How much could I actually buy with this money in today's terms?" If $500,000 is your nominal balance in 20 years and inflation averaged 3%, the real value is approximately $277,000 — meaning your purchasing power is equivalent to $277,000 today, not $500,000. The nominal amount is real money in your account; the real value is context for what it's worth.

Purchasing power is the real-world quantity of goods and services a sum of money can buy. Inflation reduces this systematically over time — not because money leaves your account, but because prices rise and each dollar stretches less far. At a consistent 3% annual inflation rate, purchasing power is cut roughly in half in about 24 years (the rule of 72: 72 ÷ 3). A $1,000,000 nominal portfolio in 30 years represents approximately $412,000 in today's purchasing power at that same rate. The erosion compounds in reverse, just as investment returns compound forward: each year's price increase applies to an already-elevated price level. A 3% annual rise over 30 years doesn't produce 90% total inflation — it produces 143% (1.03^30 − 1). This is why long-term projections can look large on paper while representing a more modest real improvement in living standards. Importantly, this is not money lost — your portfolio contains the full nominal balance. The erosion figure is a translation: it tells you what that balance is worth in today's terms, so you can set realistic expectations for what financial independence at a given balance actually means in future years.

This is the first year in which your portfolio's annual return on its existing balance — calculated as portfolioValue × annualReturnRate — equals or exceeds that year's total contribution. Before this year, deposits are the primary driver of growth. After it, compounding takes over and your money earns more in a year than you add. This crossover, sometimes called the "snowball point," is a key milestone in long-term wealth building and is particularly sensitive to starting early and maintaining a high return rate.

The gray dashed line on the chart shows what your portfolio would hold if every contribution was kept in cash with zero return. The gap between this line and the base projection is purely the effect of compounding — no contribution differences, no initial balance differences. This visual gap widens non-linearly over time and is the clearest illustration of why time in the market matters: the same dollar contributed in year 1 compounds for much longer than a dollar contributed in year 20.

The model applies a constant return rate every year. Real investment returns are volatile — equities may return 25% one year and −15% the next. A constant rate approximates the long-run average but understates the sequence-of-returns risk: poor returns early in the investment period reduce the base on which future gains compound, which can meaningfully hurt long-term outcomes compared to what a constant-rate model predicts.

A single inflation rate is applied uniformly over the full horizon to compute the purchasing power adjustment. In practice, inflation varies year by year. The adjustment shown is an estimate, not a guarantee — actual purchasing power at the end of your horizon depends on realized inflation rates that cannot be predicted with precision.

Fund expense ratios and advisory fees can be entered in the Advanced section — they are subtracted from your annual return before any simulation is run, so their compounding drag is fully captured over your horizon. For taxable brokerage accounts, an annual tax drag field models the return reduction from dividend distributions and capital gains taxes. Tax-deferred (Traditional 401k/IRA) and Roth accounts carry no annual drag; the difference is when taxes are paid — on the way in (Roth) or on the way out (tax-deferred). When all fee fields are set to 0, the projection is a pre-fee, pre-tax upper bound.

Contributions are modeled as end-of-period deposits — each amount is added after the growth for that period is applied. Beginning-of-period deposits would produce marginally higher results because contributions earn that period's return. The difference is small across most scenarios but grows with higher return rates and shorter contribution periods (e.g., weekly vs. annual).

The nest egg is the portfolio balance you need at the moment you retire. It is calculated as the present value of a growing annuity-due: a stream of withdrawals that starts immediately at retirement and increases each year at the inflation rate to preserve purchasing power. The formula is: NestEgg = W₁ × [1 − ((1+i)/(1+r))ᵈ] / (r − i) × (1+r), where W₁ is the first nominal withdrawal (paid at retirement start), r is your expected return, i is inflation, and d is the number of retirement years. When r equals i, this simplifies to NestEgg = W₁ × d. The annuity-due convention assumes the first withdrawal occurs on day one of retirement — a conservative and realistic assumption. The nest egg grows larger when the withdrawal period is longer, when inflation is higher, or when the portfolio return is lower.

You enter your retirement income target in today's purchasing power — the amount in today's terms, not the nominal figure you'll actually withdraw. The calculator converts it to a nominal retirement-era amount using your inflation rate: NominalWithdrawal = TodaysDollars × (1 + inflation)^yearsToRetirement. Entering in today's dollars is more intuitive because you can compare directly to your current spending. A target of $80,000/yr in today's dollars at 3% inflation over 30 years becomes roughly $194,000/yr in nominal terms — but both represent the same real standard of living.

The gap is the portion of your required nest egg not already covered by your current savings. Your existing savings are projected forward to retirement: CoveredBySavings = CurrentSavings × (1 + r)^n. If this projected figure equals or exceeds the nest egg target, the gap is zero and no additional contributions are needed. Otherwise, Gap = TargetNestEgg − CoveredBySavings. All annual savings calculations are then sized to fill exactly this gap through compounding contributions over your accumulation period.

Option A (flat) solves for a single constant annual savings amount using the future value of an ordinary annuity: FV = PMT × [(1+r)ⁿ − 1] / r. Rearranged: PMT = Gap × r / [(1+r)ⁿ − 1]. Option B (growing) solves for a first-year amount that then increases at your savings growth rate each year, using the future value of a growing annuity: FV = PMT₁ × [(1+r)ⁿ − (1+g)ⁿ] / (r − g). The growing scenario typically requires a lower year-1 commitment because later, larger contributions benefit from higher compounding — but the total amount contributed is often similar. The choice between them depends on whether you prefer a predictable fixed amount or a schedule that rises alongside income.

The model applies the same annual return every year through both the accumulation and retirement phases. Real portfolio returns fluctuate — a bad sequence of returns early in retirement (when the portfolio is largest and withdrawals are starting) can deplete savings far faster than a constant-rate model suggests. This is called sequence-of-returns risk, and it is not captured here. The nest egg this calculator targets is a reasonable starting point, but many financial planners recommend building in a buffer — sizing for a 3–4% withdrawal rate rather than the portfolio's full expected return.

A single inflation rate is applied uniformly to convert today's dollars to retirement-era nominal amounts and to grow withdrawals throughout retirement. Actual inflation varies year to year and may be higher for retirees — healthcare costs, for example, have historically inflated faster than the broad CPI. The results here are estimates based on your assumption, not a guarantee of purchasing power. Using a slightly higher inflation rate (e.g., 3.5% instead of 2.5%) produces a more conservative nest egg target.

The model assumes your entire retirement income comes from your investment portfolio. It does not account for Social Security benefits, a pension, rental income, part-time work, or an inheritance. If you expect meaningful income from other sources, reduce your annual income target by that amount before entering it — for example, if Social Security will cover $30,000/yr, and you want $80,000/yr total, enter $50,000 as your portfolio income target. This produces a smaller, more accurate nest egg and lower required savings.

Contributions are modeled as a single annual deposit at the end of each year. Beginning-of-year deposits would produce marginally higher results because they compound for the full year rather than nothing in year one. For the flat scenario, the actual optimal contribution schedule is monthly (as in the Growth Projector tab), but the annual model used here is a standard simplification that slightly understates the benefit of more frequent contributions — a conservative and commonly accepted assumption for this type of planning calculation.