Article — Compound Interest Calculator
Compound interest calculator: how money grows when interest earns interest
Compound interest is interest paid on both your original principal and on previously earned interest. A $10,000 deposit at 7% per year, compounded monthly, becomes $40,387 after 20 years and $163,123 after 40 years. The first 20 years quadruple the money; the next 20 years quadruple it again. That doubling-on-doubling is the engine that turns small early savings into large eventual balances.
The calculator above shows the future value of a lump sum and optional regular contributions across any compounding frequency. The article below explains where the formula comes from, how often compounding really matters, and why credit-card debt is the dark mirror of a savings account.
What is compound interest?
Compound interest adds the period's interest back into the balance, so the next period earns interest on a larger total. The growth is exponential rather than linear. A 7% annual rate means the balance multiplies by 1.07 every year, so after 10 years it multiplies by 1.07^10 = 1.967 — nearly doubled. After 30 years the factor is 7.612.
The opposite is simple interest, which only ever pays on the original principal. Simple interest at 7% for 30 years gives a final factor of 3.10 — less than half what compounding produces. The wedge between the two is the compound interest premium, and it grows every year.
Albert Einstein is widely (and probably wrongly) quoted as calling compound interest "the eighth wonder of the world." The quote has never been traced to him in writing, but the math is real: a single dollar invested at 7% per year for 100 years becomes $867.72. Most of that growth happens in the final 30 years.
The compound interest formula
The standard compound interest formula gives the future value of a single deposit growing at a fixed rate, compounded a fixed number of times per year:
A = P (1 + r/n)^(n*t) standard compoundingA = P * e^(r*t) continuous compoundingEAR = (1 + r/n)^n - 1 effective annual rateThe variables: P is the principal, r is the nominal annual rate as a decimal, n is the number of compounding periods per year, and t is the time in years. For $10,000 at 7% compounded monthly for 20 years: 10000 * (1 + 0.07/12)^(12*20) = $40,387.
Compound interest vs simple interest
The simple interest formula is A = P(1 + r*t). It ignores compounding entirely — the interest each year is the same dollar amount, never paying interest on previous interest. Simple interest still exists in some contexts (short-term US Treasury bills, auto loans in some states), but most savings, mortgages, and credit cards use compounding.
The $16,000 gap is the compound interest premium over 20 years. Stretch the horizon to 40 years and the same principal grows to $163,123 with monthly compounding versus $38,000 with simple interest — a $125,000 gap from the same starting deposit and rate.
Compound interest and compounding frequency
The compounding frequency — annual, monthly, daily, or continuous — affects the final balance but less than most people expect. The difference between annual and monthly compounding is real; the difference between daily and continuous is negligible.
- $1,000 at 5% for 1 year:
- Annual = $1,050.00 (the base case)
- Semi-annual = $1,050.63 (gain: 63 cents)
- Quarterly = $1,050.95 (gain over annual: 95 cents)
- Monthly = $1,051.16 (gain over annual: $1.16)
- Daily = $1,051.27 (gain over annual: $1.27)
- Continuous = $1,051.27 (the theoretical maximum)
The marginal gain shrinks because the per-period rate shrinks as fast as the period count grows. Once you reach daily compounding, going further adds fractions of a cent. Continuous compounding (the mathematical limit using Euler's e) sits a hair above daily.
Regular contributions and compound growth
Most real savings accounts combine a starting deposit with ongoing contributions. Each contribution itself starts compounding from the moment it lands. The calculator handles this by treating monthly contributions as end-of-month deposits, then growing each one at the configured rate.
The effect is dramatic. $10,000 at 7% compounded monthly for 20 years with no further deposits grows to $40,387. Add $200 a month and the balance reaches about $145,000 — the contributions total $48,000 but compounding earns an extra $96,000 on top. Time, not rate, is the dominant lever once contributions are involved.
Starting 10 years earlier almost always beats contributing 10 years longer. Someone who saves $200 a month from age 25 to 35 (then stops) typically ends up with more at retirement than someone who saves the same amount from 35 to 65, because the early contributions have so much more time to compound.
Rule of 72 and doubling time
The Rule of 72 is a quick mental shortcut for compound growth: divide 72 by the annual percentage rate to get the approximate number of years until the money doubles. At 6% it takes about 12 years; at 8%, about 9 years; at 12%, about 6 years.
The Rule is most accurate for rates between 4% and 12%. Outside that range it drifts: at 2% the true doubling time is 35 years (Rule says 36); at 15% it is 4.96 years (Rule says 4.8). The mathematical exact version is ln(2)/ln(1+r) which gives the true doubling factor.
Compound interest on debt
Compound interest cuts both ways. On savings it makes money grow; on debt it makes balances grow at the same rate. Credit cards typically compound daily on the average daily balance, with APRs commonly between 18% and 29%. At a 24% APR with daily compounding, an unpaid $5,000 balance grows to about $6,357 after one year — $1,357 in interest, all from doing nothing.
Making only the minimum monthly payment on a credit card at 24% APR can keep a balance growing for decades. A $5,000 balance at the typical 2% minimum payment would take roughly 22 years to pay off and cost over $6,000 in interest. Paying just $100 more per month cuts the time to under 5 years.
Common compound interest mistakes
The most common error is confusing the nominal annual rate (APR) with the effective annual rate (APY or EAR). A "5% savings account" usually means 5% APR with monthly compounding, which yields 5.116% per year. Most savings ads now use APY by regulation, but loan products still quote APR, and the two are not interchangeable.
A second mistake is underestimating long horizons. Linear intuition expects 30 years of 7% to triple your money. Compound math nearly octuples it. The third mistake is ignoring fees: a 1% annual management fee on an investment account compounds against you in exactly the same way returns compound for you, and over 30 years can eat 25% of the eventual balance.