What compound interest does
Compound interest = your money earning interest on its previous interest.
A simple example: $1,000 at 10% APR for 3 years.
- Simple interest: $1,000 + (3 × $100) = $1,300
- Compound interest: $1,000 × 1.1³ = $1,331
The $31 difference is small over 3 years. Over 30 years, it explodes:
- Simple: $1,000 + (30 × $100) = $4,000
- Compound: $1,000 × 1.1³⁰ = $17,449
That’s the famous “compounding is the eighth wonder of the world” effect. The longer the timeframe, the more dramatic.
With monthly contributions
If you also contribute $100/month to that 10% account for 30 years, the math gets even more interesting:
- Total you contributed: $1,000 + ($100 × 12 × 30) = $37,000
- Total final value: ~$245,000
- Compounding earned you ~$208,000 — more than 5× what you put in.
That’s why retirement accounts (401k, IRA, Roth IRA, HSA) work so well — long time horizons + monthly contributions + compounding. Starting at 25 vs 35 with the same monthly contribution typically results in 2-3× more at retirement.
Realistic interest rates (US, 2026)
- High-yield savings (HYSA): 4-5% APR — short-term, FDIC-insured
- CDs (1-5 year): 4-5% — locked-up savings
- Treasury bonds (10y): 4-5% — government debt
- Corporate bonds: 5-7% — higher yield, default risk
- S&P 500 historical: ~10% nominal, ~7% real (after inflation), but with high volatility — short timeframes can see -30%+ years
- Real estate (REITs): 8-10% historical including dividends
For long-term retirement planning, 7% real (inflation-adjusted) is the standard conservative assumption.
Compounding frequency — does it matter?
Marginal at most rates and timeframes. The differences:
- Annual compounding: 1 + r once per year
- Monthly compounding: (1 + r/12)^12 ≈ 1 + r + tiny bit more
- Daily compounding: (1 + r/365)^365 ≈ 1 + r + slightly more
At 7% annual rate over 20 years: $1,000 grows to $3,870 (annual) vs $4,022 (monthly) vs $4,055 (daily). Real impact: a few percent over decades. Most savings accounts compound daily; investment accounts compound continuously through reinvestment of dividends/interest.
Related calculators
- FIRE calculator — financial independence number
- Hourly to salary — annual income calculator
- Net profit margin — business profitability
- Pay raise — salary increase impact
Sources
- SEC investor.gov — Compound Interest Calculator
- Investopedia — Compound Interest
- Federal Reserve Economic Data (FRED)
The Rule of 72
A famous mental shortcut for compound growth:
Years to double = 72 ÷ interest rate
So at 7% APR: 72/7 ≈ 10.3 years to double your money. At 10% APR: 72/10 = 7.2 years. At 4% APR: 72/4 = 18 years.
Useful for back-of-napkin retirement projections.
Realistic US tax-advantaged accounts
For long-term compounding, tax-advantaged accounts compound dramatically faster than taxable accounts:
- Roth IRA: $7,000/year (2025) — tax-free growth and withdrawals
- Traditional 401(k): $23,500/year (2025), often with employer match — pre-tax contributions
- HSA: $4,300 self / $8,550 family — triple-tax-advantaged with HDHP
- Roth 401(k): $23,500/year — same limits as traditional but post-tax
A 30-year-old maxing Roth IRA + 401(k) at $30k/year for 30 years at 7% real returns ends with ~$3M in 2025 dollars.
Last verified: April 2026.