How to Use This Calculator
- Projection ??see what your portfolio could grow to. Inflation converts the nominal number to today's dollars; the tax field reduces total gain at the end.
- Required Return ??given a target, time, and contribution, solve for the rate of return needed. If the answer is much higher than long-run market returns (~7??0% for U.S. stocks), the goal probably needs more time or more contribution rather than chasing higher returns.
- Time to Goal ??given a return, how long until the target is reached.
- Compare ??quickly see the dollar impact of, say, a 6% vs. 8% return over 20 years, or a $500 vs. $1,000 monthly contribution.
Future Value Formula
The closed-form future value of an investment with periodic contributions is:
The Projection tab uses this formula directly. The Required Return and Time to Goal tabs invert it ??Required Return uses a numerical solver (bisection), Time to Goal solves analytically when possible and falls back to bisection.
Historical U.S. Market Returns
The S&P 500 has returned roughly 10% per year nominally / 7% real over the long run, with substantial year-to-year variation including drops of 30%+ in some years.[1] A diversified 60% stock / 40% bond portfolio has historically returned about 7??% nominal, with smaller drawdowns. Pick a return assumption you can stomach if it disappoints ??and stress-test by reducing it by 1?? points.
Tax Drag and the Account Wrapper
Where you hold the investment changes the after-tax outcome:
- Taxable brokerage ??dividends and realized gains are taxed in the year they occur. Long-term capital gains (held > 1 year) are taxed at 0%, 15%, or 20% federally.[2]
- Traditional 401(k) / IRA ??contributions are pre-tax; withdrawals in retirement are taxed as ordinary income.
- Roth 401(k) / Roth IRA ??contributions are post-tax; qualified withdrawals are tax-free.
- HSA ??pre-tax in, tax-free out for medical; treated like a traditional IRA after 65 for non-medical.
The Projection tab's Tax field is a simple end-of-period haircut and works best for a single long-term-gain realization at exit.
Inflation and Real Value
The Fisher relation links nominal and real growth:
$1,000,000 nominal in 30 years at 3% inflation is worth about $412,000 in today's purchasing power.[3]
Frequently Asked Questions
Does this calculator know my actual returns?
No. It applies the rate you provide as a constant annual figure. For path-dependent stress tests, run the Projection tab twice ??once at your central estimate, once 1?? points lower.
What return should I assume?
A common middle-ground for U.S. equity-heavy portfolios is 7% nominal (after fees), 4% real. Bond-heavy portfolios are typically 4??% nominal.
Why are the numbers so sensitive to small return changes?
Compound growth is exponential. A 2-point difference over 30 years is roughly a 2횞 difference in ending balance. That's why fees and tax drag matter so much.
References
- [1] Wikipedia, "S&P 500" ??historical annual returns (CC BY-SA 4.0). en.wikipedia.org/wiki/S%26P_500
- [2] U.S. Internal Revenue Service ??Topic 409 Capital Gains. irs.gov/taxtopics/tc409
- [3] U.S. Bureau of Labor Statistics ??CPI. bls.gov/cpi
Educational content on this page is original prose written for MODOO. Material referenced from Wikipedia is used under the CC BY-SA 4.0 license.