Compound Interest Calculator

A daily latte habit redirected to a low-cost index fund is the most accessible way to feel exponential growth in everyday numbers. Make it concrete: $5 per day equals $150 per month. Invest that $150 monthly from age 25 to 65 in a broadly diversified equity index — historically, the S&P 500 total-return series has averaged roughly 10% nominal and roughly 7% real (inflation-adjusted) over the long run, per data compiled by NYU's Aswath Damodaran from CRSP and S&P Global. Use the future-value-of-an-annuity formula: FV = PMT × [((1 + r/n)^(nt) − 1) / (r/n)] × (1 + r/n) for end-of-month compounding. With PMT = 150, r = 0.10, n = 12, t = 40 you arrive at approximately $948,000 nominal. At 7% real, the same contribution lands near $395,000 in today's dollars — still about $123,000 of contributions for $272,000 of real purchasing-power growth. Start late and the math is unforgiving. Starting at 35 with the same $150/month and same 10% nominal return → ≈ $342,000 at 65. Starting at 45 → ≈ $114,000. The first decade of compounding produces almost half of the final balance because the early dollars get the most doublings. The Rule of 72 makes this intuitive: at 10% returns money doubles every ~7.2 years. From age 25 to 65 you get roughly 5.5 doublings; from 35 you get 4.2; from 45 you get only 2.8. Each missed doubling halves your future amount. Bumping the contribution turns the math from "interesting" into "life-changing." $300/month from age 25 reaches roughly $1.9M nominal; $500/month reaches roughly $3.2M. The math scales linearly with PMT but exponentially with time, so adding years matters more than adding dollars in the early decades. The real-world friction is fees: a 1% annual expense ratio (typical for an actively managed fund) reduces the 40-year FV by roughly 25%. Vanguard VTI (total US stock market) carries a 0.03% expense ratio. iShares ITOT carries 0.03%. Schwab SCHB carries 0.03%. Three basis points compound trivially; 100 basis points compound dramatically. Honest caveats. (1) The 10% historical average comes with ~19% annual standard deviation, meaning any specific 5-year window can easily return 0% or negative 30%. The math here is an expected long-run path, not a guarantee. (2) Sequence-of-returns risk matters most near retirement — a major drawdown at age 60 can lock in losses that a drawdown at 30 would have recovered from. (3) Taxes erode after-tax returns; using a Roth IRA or 401(k) shelters compounding from drag. This is general educational illustration, not financial advice; for personalized planning consult a fiduciary financial advisor.

// Future value of $150/month at 10% nominal, monthly compounding
function annuityFV(PMT, rate, years, n = 12) {
  const r = rate / n, k = n * years;
  return PMT * ((Math.pow(1 + r, k) - 1) / r) * (1 + r);
}

annuityFV(150, 0.10, 40); // ~948,000 starting at age 25
annuityFV(150, 0.10, 30); // ~342,000 starting at age 35
annuityFV(150, 0.10, 20); // ~114,000 starting at age 45

// Same payment, just less time -> roughly half as much for each decade lost.
// Real (inflation-adjusted) at 7%:
annuityFV(150, 0.07, 40); // ~395,000 in today's dollars

Both Roth and Traditional IRAs use compound growth, but the timing of taxes splits the future-value math in subtle ways. Traditional IRA contributions are pre-tax — your $7,000 contribution lowers this year's taxable income by $7,000. The entire balance, including future gains, gets taxed as ordinary income at withdrawal. Roth IRA contributions are post-tax — you contribute $7,000 of after-tax money, but every dollar of future growth and every dollar of qualified withdrawal is tax-free. The 2026 IRS contribution limit is $7,000 for under-50, $8,000 with the catch-up. The clean comparison most articles miss: if your marginal tax rate is identical at contribution and at withdrawal, Roth and Traditional produce mathematically identical after-tax wealth. Proof: let M be your marginal rate, P your contribution amount, r the annual return, t the years. Traditional grows the full pre-tax amount and pays tax at the end: after-tax FV = P × (1+r)^t × (1−M). Roth pays tax at the start and grows tax-free: after-tax FV = P × (1−M) × (1+r)^t. The two expressions are algebraically the same. The break is only when M differs over time. So which is better in practice? Roth wins when your future tax rate will be higher than today — typical for early-career professionals expecting income growth, residents of states with no income tax who plan to retire in a higher-tax state, or anyone who believes federal rates rise over time (the Tax Cuts and Jobs Act 2017 reductions sunset after 2025 absent new legislation). Traditional wins when your future rate will be lower — typical for high earners in their peak income years (32–37% federal bracket today) who expect to retire in the 12–22% bracket. Many financial planners recommend a mix to hedge tax-rate uncertainty. The hidden Roth advantage that breaks the symmetry: Roth has effectively higher contribution capacity. A $7,000 Roth contribution shelters $7,000 of after-tax dollars from future tax. A $7,000 Traditional contribution shelters $7,000 minus future tax. To match the after-tax shelter of a Roth at a 30% future rate you would need to contribute $10,000 in Traditional — but the IRS cap is the same $7,000 for both. So at the cap, Roth always shelters more real wealth. There are also no required minimum distributions on Roth IRAs (Traditional IRAs require RMDs starting at age 73), and Roth lets you withdraw your contributions (not earnings) anytime tax- and penalty-free. Income limits matter. The 2026 Roth IRA contribution phases out between $150,000 and $165,000 modified AGI for single filers ($236,000–$246,000 for married-filing-jointly). Above the cap you cannot contribute directly, but the "backdoor Roth" — non-deductible Traditional contribution converted to Roth — remains legal under current law. This is general education only; consult a CPA or fee-only financial planner for personalized tax strategy.

// Equal tax rates: Roth and Traditional produce identical after-tax wealth.
const P = 7000, r = 0.10, t = 30;
const M = 0.24; // marginal rate at contribution = at withdrawal

const traditional = P * Math.pow(1+r, t) * (1 - M);  // 92,832
const roth        = P * (1 - M) * Math.pow(1+r, t);  // 92,832 (identical)

// Different rates -> winner depends on direction
const Mnow = 0.32, Mlater = 0.18;  // high earner now, low later
const trad2 = P * Math.pow(1+r, t) * (1 - Mlater); // 100,237
const roth2 = P * (1 - Mnow) * Math.pow(1+r, t);   // 83,128
// Traditional wins: $17,109 more after-tax wealth

// Reverse: starting low, expecting higher future rate
const Mlow = 0.12, Mhigh = 0.28;
P * Math.pow(1+r, t) * (1 - Mhigh); // 87,997 traditional
P * (1 - Mlow) * Math.pow(1+r, t);  // 107,615 roth -> Roth wins

A 529 plan is a state-sponsored, tax-advantaged investment account purpose-built for education expenses. Contributions are made with after-tax dollars (similar to a Roth), grow federally tax-free, and qualified withdrawals — tuition, fees, books, room and board, and up to $10,000/year of K–12 tuition under the 2017 TCJA expansion — are also federally tax-free. Many states layer on a state income tax deduction for contributions to their own plan: New York, Illinois, Michigan, and several others offer deductions worth several hundred to a few thousand dollars annually. The compounding case is strong because the planning horizon is naturally long. Open a 529 at a child's birth and you have 18 years before tuition starts — long enough for two doublings at 7% real returns. Contribute $300/month from birth to age 18 and the balance lands near $130,000 nominal at 8% (a typical age-based portfolio's return historically). Even $100/month becomes roughly $43,000 over the same span. The earlier the start, the more aggressive the equity allocation can be in early years, gradually de-risking via the plan's "age-based" or "target-enrollment-date" glide path as college approaches — much like a target-date retirement fund. Real cost numbers anchor the planning. The College Board's Trends in College Pricing 2024 report puts the average published in-state public four-year tuition at roughly $11,260/year and four-year private at roughly $43,350/year (excluding room and board, books, fees). Assume 4% annual tuition inflation — close to historical average per the College Board, though specific years vary widely — and a public four-year sticker price for a child born in 2026 would be around $22,800/year by freshman year, or roughly $95,000 across four years. A private four-year would be around $87,800/year, or $367,000 total. These are sticker prices; actual net price after grants and scholarships is typically much lower. Important constraints. (1) Non-qualified withdrawals trigger ordinary income tax on the earnings portion plus a 10% federal penalty (with several exceptions including scholarships, death, disability, and military academy attendance). (2) 529 balances count as a parental asset on the FAFSA at a maximum 5.64% rate — far gentler than the 20% rate applied to student-owned assets. (3) The SECURE 2.0 Act (2022) added a path to roll up to $35,000 of unused 529 balance into a beneficiary's Roth IRA after the account has been open 15 years, subject to annual Roth contribution limits — meaning over-funding is less catastrophic than it used to be. (4) Investment options are limited to whatever menu your chosen state plan offers; expense ratios range from 0.10% (Utah my529, Nevada Vanguard 529) to 1.5%+ for some advisor-sold plans — choose direct-sold plans with low fees. Educational only; consult a CPA or fee-only financial planner for state-specific tax strategy.

// 529 plan: contributions from birth to age 18
function plan529(monthly, returnPct) {
  const r = returnPct / 12, n = 12 * 18;
  return monthly * ((Math.pow(1+r, n) - 1) / r) * (1 + r);
}

plan529(100, 0.08); // ~$43,400 (modest)
plan529(300, 0.08); // ~$130,200 (covers ~6 yrs in-state public)
plan529(500, 0.08); // ~$217,000 (covers most private 4-yr)

// Future tuition with 4% inflation
function futureCost(currentAnnualCost, years, inflation = 0.04) {
  return currentAnnualCost * Math.pow(1 + inflation, years);
}
futureCost(11260, 18);  // ~$22,800/yr public 4-year by freshman year
futureCost(43350, 18);  // ~$87,800/yr private 4-year by freshman year