See how your savings grow with monthly contributions and any compounding frequency — daily, monthly, quarterly, or annually. Updated for 2026.
Compound interest is interest you earn on both your original deposit and the interest that has already accumulated. Each compounding period, the bank or investment adds interest to your balance, and the next period's interest is calculated on the new (larger) balance. Over long horizons this snowball effect dramatically outperforms simple interest.
Simple interest pays the same dollar amount every period. A $10,000 deposit at 7% simple interest for 10 years earns exactly $700 each year, totaling $17,000 at the end. The same deposit at 7% compounded annually grows to $19,672, and at 7% compounded monthly reaches $20,097. The extra $3,097 comes purely from interest earning interest.
The standard future-value formula with no contributions is:
A = P × (1 + r/n)n·t
When you also add a fixed contribution PMT each period, the formula becomes the future value of an annuity plus the future value of the lump sum:
A = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) ÷ (r/n)]
The Rule of 72 is a fast mental shortcut: divide 72 by your annual rate (as a whole number) to estimate how many years your money takes to double. At 6%, that's 72 ÷ 6 = 12 years; at 9% it's 8 years. The Rule of 70 is slightly more accurate for low rates and continuous compounding, and the Rule of 114 estimates time to triple.
| Rate | Rule of 72 (double) | Rule of 114 (triple) | Exact double |
|---|---|---|---|
| 3% | 24 yrs | 38 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 |
$10,000 deposited at 7% with no contributions grows to:
Daily compounding is only 2.4% better than annual at 7%. At lower rates the gap shrinks further. This is why APY (Annual Percentage Yield), which standardizes for compounding frequency, is the apples-to-apples comparison metric required on U.S. savings products by the Truth in Savings Act.
APR (Annual Percentage Rate) is the simple annual rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding. A bank advertising "6.00% APR compounded monthly" actually delivers an APY of (1 + 0.06/12)12 − 1 = 6.168%. Always compare savings accounts by APY, not APR.
Inflation also compounds. At 3% annual inflation, $100 today only buys $74.41 worth of goods in 10 years. To compute real (inflation-adjusted) returns, subtract the inflation rate from your nominal rate: a 7% nominal return with 3% inflation is approximately a 3.88% real return (Fisher equation: 1.07 ÷ 1.03 − 1).
The standard future-value formula with regular contributions is A = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) ÷ (r/n)]. P is principal, r is the annual rate as a decimal, n is the number of compounding periods per year, t is years, and PMT is the per-period contribution.
It matters a little but not much. On a $10,000 deposit at 7% for 10 years, annual compounding produces $19,671, monthly $20,097, and daily $20,138 — about a 2.4% gap between annual and daily.
It is a mental shortcut: divide 72 by the annual interest rate to estimate years required to double your money. At 8%, money doubles in roughly 72 ÷ 8 = 9 years.
In a taxable account, interest is taxed each year as ordinary income (in the U.S.). Inside a Roth IRA, Roth 401(k), or HSA used for qualified medical expenses, growth is tax-free. Inside a Traditional IRA or 401(k), growth is tax-deferred until withdrawal.
The S&P 500 has averaged ~10% nominal and ~7% real (inflation-adjusted) annualized total return since 1928. For conservative planning, model 6–7% real returns.
It applies the textbook formula with constant rate and constant contribution assumptions. It does not include taxes, inflation, fees, or variable rates. For pre-tax projections at a constant rate it is mathematically exact.
APR is the simple annual rate without compounding. APY (Annual Percentage Yield) includes compounding. A 6% APR compounded monthly is approximately 6.17% APY.
This tool models a growing asset where compound interest works in your favor. For loans where compounding works against you, use our Loan Calculator or Amortization Calculator.
Disclaimer: ProCalcVerse calculators are for educational and informational purposes only and do not constitute financial advice. Consult a licensed financial planner for personalized guidance.