See how your savings grow with monthly contributions and any compounding frequency — daily, monthly, quarterly, or annually. Updated for 2026.
Albert Einstein almost certainly never called compound interest "the eighth wonder of the world." The quote is apocryphal — finance writers have been chasing the citation for a hundred years without finding it. What is real is that compound interest is the single most powerful arithmetic relationship a long-horizon saver controls. Get the equation right, and roughly half the work of building wealth takes care of itself.
Compounding is what happens when interest you've already earned starts earning interest of its own. Each compounding period — daily, monthly, quarterly, or annually — the bank, fund, or brokerage credits you with the period's interest based on your current balance, including all previously credited interest. The next period's interest is then calculated against the new (larger) balance, and so on.
That recursive layering is what separates compound interest from simple interest. Simple interest pays a flat dollar amount each period based only on the original principal. A $10,000 deposit at 7% simple interest pays $700 a year — every year, forever — totaling $17,000 after 10 years. The same deposit at 7% compounded annually reaches $19,672; compounded monthly, $20,097. The extra $3,000 came purely from interest earning interest.
The future-value equation with a lump sum and regular contributions has two terms:
A = P(1 + r/n)nt + PMT × [ ((1 + r/n)nt − 1) ÷ (r/n) ]
The first term is straightforward future-value math. The second is the future value of an "annuity" — financial-textbook language for a series of equal payments. Together they produce the total balance at the end of period t.
That's an ordinary 401(k) contribution path, not an aggressive one. The thing doing the heavy lifting isn't an unusual return assumption — it's the 28-year runway.
People reflexively try to optimize the rate (chasing yield, switching funds, picking stocks). They under-invest in time, which is the variable that compounds exponentially. Two illustrative paths to age 65:
Investor B contributed three times as much money and finished with roughly two-thirds the balance. The only difference was a 10-year head start. This is why financial planners obsess over compound starting age — there is no rate that fixes a missing decade.
The Rule of 72 is a mental shortcut to estimate how long your money takes to double: divide 72 by your annual rate. At 6%, money doubles in roughly 12 years. At 9%, around 8 years. The Rule of 70 is slightly more accurate for low rates and continuous compounding; the Rule of 114 estimates the time to triple.
| Rate | Rule of 72 (double) | Rule of 114 (triple) | Exact double |
|---|---|---|---|
| 3% | 24.0 yrs | 38.0 yrs | 23.4 yrs |
| 5% | 14.4 yrs | 22.8 yrs | 14.2 yrs |
| 7% | 10.3 yrs | 16.3 yrs | 10.2 yrs |
| 10% | 7.2 yrs | 11.4 yrs | 7.3 yrs |
Hardly. The same $10,000 at 7% for 10 years grows to:
The daily-vs-annual gap is about 2.4% on a 10-year horizon and shrinks at lower rates. This is why the U.S. Truth in Savings Act requires banks to quote APY (effective rate after compounding) instead of just the headline rate — it standardizes the comparison so consumers don't have to do the math.
Inflation is also a compounding machine, just one that runs against you. If you earn 7% nominal in a year of 4% inflation, your real return is about 2.88%. The Fisher equation handles the conversion precisely:
Real return = (1 + Nominal) ÷ (1 + Inflation) − 1
For long-horizon planning, always project in real terms (return minus inflation). A common retirement-planner default: 7% nominal stock returns minus 3% inflation = 4% real. Use the higher number only if you want to be optimistic and re-check your projections later.
Simple interest pays a flat amount each period based only on the original principal. Compound interest pays interest on both the principal and all previously credited interest, so each period's growth is slightly larger than the last.
Most U.S. banks compound interest daily on deposits and post it to the account monthly. The Truth in Savings Act requires daily compounding for FDIC-insured savings products to be quoted in APY terms.
No. It computes pre-tax, pre-fee growth at the input rate. For taxable accounts, multiply the rate by (1 − your marginal tax rate) before entering it to model after-tax growth. For fees, subtract the expense ratio from the rate.
6% to 7% real (inflation-adjusted) for diversified U.S. equity exposure. If you input nominal returns instead, plan to subtract 2.5% to 3.5% for inflation when comparing future amounts to today's purchasing power.
For modeling purposes this calculator assumes end-of-period contributions credited at each compounding cycle. Real-world brokerages typically credit on the trade-settlement date; banks credit at the daily cycle close. The difference is tiny over multi-year horizons.
Yes. Treat the 529 like any other tax-advantaged account. Just remember 529 growth is tax-free only for qualified education expenses; non-qualified withdrawals owe income tax plus a 10% penalty on the earnings portion.
Continuous compounding — the limit as n approaches infinity — is governed by e^(rt). At 7% for 10 years, continuous compounding gives e^0.7 = 2.0138, identical to daily compounding to four decimal places.
Yes — on the borrower side, the exact same formula works against you. The Loan Calculator and Amortization Calculator show how compounding shapes the total cost of debt.
Editorial note: This calculator and accompanying article are educational and do not constitute personalized investment advice. Returns from any specific account, fund, or security are not guaranteed, and historical patterns do not predict future results. Consult a fee-only CFP® or fiduciary investment advisor for portfolio-specific recommendations. Last reviewed by Priya Venkatesan, CFA, on March 4, 2026.