SOLVETUTORMATH SOLVER

Instrument MI-02-489 · Finance

Retirement Calculator

Two numbers already growing — what you've saved and what you add each month — compounded forward at one flat rate to see what waits at Years until retirement.

Instrument MI-02-489
Sheet 1 OF 1
Rev A
Verified
Type 02 — Retirement SER. 2026-02489

Projected retirement balance, $

$691,306.76

FV = PV(1+r)ᴺ + PMT·((1+r)ᴺ − 1) ⁄ r

The working Every figure verified twice
  1. futureValue = 50000·(1 + 7 ⁄ 1200)^(25·12) + 500·(((1 + 7 ⁄ 1200)^(25·12) − 1) ⁄ (7 ⁄ 1200)) = 691,306.76
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

This sheet compounds two separate streams into one number. Current retirement savings, $ behaves like a single deposit left alone: it multiplies by (1 + r) once for every month between today and retirement, so it grows purely from the passage of time and the assumed rate. Monthly contribution, $ is a second, smaller stream — a fresh deposit added every month that only gets however many months remain to compound, so the first dollar contributed earns far more growth than the last one. The two streams are computed separately and added, which is why the worked example below can be checked in two independent pieces rather than trusted as one opaque total.

Both streams run on the same clock: r takes Expected annual return, % and splits it into twelfths, while the exponent takes Years until retirement and counts it in months instead of years, so the arithmetic compounds monthly even though the two inputs you actually set are yearly. That convention matters — spreading an annual rate across twelve monthly credits returns slightly more over a year than the flat annual figure alone, because interest earned in January starts earning its own interest in February. A saver reading a statement that credits interest monthly is looking at exactly this mechanic, not a rounding quirk.

Nothing here distinguishes a 401(k) from an IRA or an ordinary brokerage account, and that is deliberate: Current retirement savings, $ and Monthly contribution, $ can represent one account or the sum of several, since the compounding math does not care which paperwork holds the money. Left out on purpose are taxes, fees, employer matching, contribution limits set by the IRS, and any assumption that the return or the contribution amount ever changes — Expected annual return, % is held flat for the entire span, which no real portfolio delivers year after year.

FV=PV(1+r)N+PMT(1+r)N1rFV = PV(1+r)^{N} + PMT \cdot \frac{(1+r)^{N} - 1}{r}r=annualReturn1200,N=yearsToRetirement×12r = \frac{\text{annualReturn}}{1200}, \quad N = \text{yearsToRetirement} \times 12
FV — Projected retirement balance, $ · PV — Current retirement savings, $ · PMT — Monthly contribution, $ · r — the monthly rate, found by taking Expected annual return, % ⁄ 1200 · N — the number of months, found by taking Years until retirement × 12.
  • Enter what you have saved today into Current retirement savings, $ — the lump sum already sitting in your accounts.
  • Set Monthly contribution, $ to the amount you add every month, not an annual or per-paycheck figure.
  • Type the single flat rate you expect the balance to earn into Expected annual return, %.
  • Enter Years until retirement — the count of full years the money has left to compound.
  • Read Projected retirement balance, $ for what the two streams reach combined, right after the final month's contribution lands.

Worked example — $50,000 plus $500 a month for 25 years

Set Current retirement savings, $ to 50000, Monthly contribution, $ to 500, Expected annual return, % to 7, and Years until retirement to 25 — the sheet's own defaults. The monthly rate works out to r = 7 ⁄ 1200 = 0.5833%, and the exponent becomes N = 25 × 12 = 300 months. Projected retirement balance, $ reads $691,306.76.

Split that figure to see why it holds together. The $50,000 already saved grows alone to $286,270.91 over those same 300 months at that rate — plain lump-sum compounding, nothing added along the way. The $500-a-month stream, run through the same 300 months with each deposit earning only however many months remain after it lands, reaches $405,035.85 on its own. Add the two pieces: $286,270.91 plus $405,035.85 equals $691,306.76, the same figure the sheet returns in one step.

Questions

Why does the formula compound monthly instead of once a year?

Because the two inputs you set — Monthly contribution, $ and Years until retirement — describe a monthly habit over a span of years, the sheet turns Expected annual return, % into a monthly rate (divided by 1200) and turns years into months (times 12) before compounding. A once-a-year model would credit interest only twenty-five times over 25 years instead of three hundred, understating what a monthly-crediting account actually pays.

Does raising the years or raising the monthly contribution help more?

Years usually help more, because Years until retirement sits inside the exponent while Monthly contribution, $ only multiplies the outside of the formula. Doubling the contribution doubles the annuity portion of the result exactly; adding years compounds growth on top of growth, so the same monthly amount left to run longer typically outpaces the same dollars added later at a higher monthly rate.

Will the sheet stop me from entering more than legal contribution caps?

No. Monthly contribution, $ is compounded exactly as typed, with no comparison against 401(k) elective-deferral caps, IRA annual limits, or any employer plan's rules. If your savings are split across several accounts, each with its own legal ceiling, add the totals yourself before entering a combined figure here.

Why doesn't this ask about a 401(k) employer match?

Because Current retirement savings, $ and Monthly contribution, $ are meant to represent whatever you already have and add across any account — 401(k), IRA, taxable brokerage, or a mix — without assuming one specific plan's rules. A calculator built around a single employer plan would add a matching-percentage field and a vesting schedule; this one stays deliberately generic so the two figures can represent a combined total.

Is Expected annual return, % guaranteed to happen?

No — it is a single flat assumption you supply, held constant for every month in the span. Real portfolios move up and down year to year, and a rate that looks reasonable averaged over decades can still produce stretches of loss along the way. Treat Projected retirement balance, $ as what a steady, hypothetical rate would deliver, not a promised outcome.

What costs or events does this arithmetic leave out?

Taxes on withdrawals or gains, account fees, inflation eating into future purchasing power, Social Security or pension income, and any change to Monthly contribution, $ over time are all left out. The sheet performs one calculation — two compounding streams added together — and nothing more; everything else that affects a real retirement is a separate question.

References

Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.