How compound interest works
Each period’s interest is added to the balance, and the next period’s interest is figured on that larger balance. Put $10,000 in an account paying 5% a year, compounded annually, and the first year earns $500. The second year earns $525, because it is paid on $10,500, and the third earns $551.25.
The extra dollars look trivial at first, but the gap keeps widening because growth is proportional to the balance. Investor.gov makes the point with a dollar a day: $365 saved once and left to earn 5% a year grows to $465.84 after five years and to $1,577.50 after 30.
Three levers set the result: the rate, the time, and how much you start with or keep adding. Time is the one you cannot make up later, because the largest yearly gains arrive at the end, when the balance is biggest. That is why starting early matters more than most people expect, and why compounding sits under the time value of money, the method for comparing dollars paid at different dates.
Compound interest vs. simple interest
Simple interest is paid only on the original principal: interest = principal × rate × years. At 5%, $10,000 earns a flat $500 every year, so it reaches $15,000 after 10 years and $25,000 after 30. Compounded once a year at the same 5%, it reaches $16,288.95 after 10 years and $43,219.42 after 30, and the table below shows the gap still widening at 40. The rate is identical; the whole difference is interest earning interest.
Simple interest still shows up in practice whenever interest is paid out instead of added to principal. Treasury notes and bonds, for example, pay their interest in cash every six months, and a coupon you spend does not compound. What happens to each payment decides the growth you see: reinvest it and you rebuild compounding yourself; spend it and the balance stays flat. The same logic applies to dividends and fund distributions, which is why published total returns assume they are reinvested.
How compounding frequency and APY work
Interest can be credited yearly, semiannually, monthly or daily, and each bank sets its own schedule. The more often it is credited, the sooner each slice of interest starts earning its own interest, so the same quoted rate produces slightly more money. The effect is real but small: at a 5% rate, annual compounding yields 5.00% a year and daily compounding about 5.13%, so $10,000 left for 10 years ends at $16,486.65 instead of $16,288.95, about $198 more.
To make accounts comparable, the federal Truth in Savings rules (Regulation DD) separate two numbers. The interest rate, the stated or nominal rate, does not reflect compounding. The annual percentage yield, or APY, reflects both the rate and the frequency of compounding over a 365-day year, assuming principal and interest stay on deposit. Two accounts with the same APY pay the same over a year whatever their schedules, so compare a high-yield savings account with a CD by APY, not by rate.
I bonds and EE bonds compound semiannually: every six months the rate is applied to a new principal that includes the interest earned so far. Loans follow separate disclosure rules, so a loan’s APR is not the same measure as a deposit account’s APY.
Compounding in investments: growth on growth
Stocks and funds do not pay interest, but they compound the same way when gains stay invested: reinvested dividends buy more shares, and next year’s price change applies to the bigger holding. Investors call this compound growth or compound returns. The difference from a savings account is that the rate is not fixed. Returns vary from year to year, losses compound too, and the steady rate that describes a bumpy history is its compound annual growth rate, which is usually lower than the simple average of the yearly returns.
Anything that trims the rate every year also compounds. A fund’s expense ratio and the yearly tax on distributions in a taxable account, often called tax drag, shrink the rate at which the whole balance grows, not just one year’s gain. Inflation compounds as well, which is why planners judge long-run growth by the real rate of return. For a quick sense of scale, the Rule of 72 turns any compound rate into an approximate doubling time.
When compounding works against you
Compounding is neutral math. It builds a debt the same way it builds savings when unpaid interest is added to what you owe and then charged interest itself. At 24% a year, compounded monthly, a balance left untouched doubles in about three years. A payment that only covers the interest leaves the balance where it started; one that falls short makes it grow. No investment reliably earns more than a high credit card rate, which is the logic behind the debt avalanche: pay off the highest-rate balance first.
Two quieter versions matter in a lifetime plan. Rising prices compound, so a fixed income loses purchasing power faster than intuition suggests: at 3% a year, $1,000 received ten years from now buys only what about $744 buys today. And money taken from an invested account early, as a fee, a penalty or an avoidable tax, forfeits all the compounding it would have done over the following decades.
Illustrative numbers
$200 a month at 6% a year, compounded monthly, for 30 years
- A
- Balance after t years
- P
- Starting principal
- r
- Annual interest rate as a decimal (5% = 0.05)
- n
- Times interest is compounded per year (1, 4, 12, 365)
- t
- Years the money stays invested
With a deposit D at the end of each period, add D × [(1 + r ÷ n)^(n × t) − 1] ÷ (r ÷ n) to A.
Monthly deposit$200 at the end of each month
Monthly rate6% ÷ 12 = 0.5%
Balance after 10 years$32,775.87 from $24,000 deposited
Balance after 20 years$92,408.18 from $48,000 deposited
Balance after 30 years$200,903.01 from $72,000 deposited
Interest earned over 30 years$128,903.01, or 64% of the balance
The last 10 years add $108,494.83, more than the first 20 years produced in total, although the deposit never changes. Start the same $200 a month 10 years later and the account ends at $92,408.18: less than half as much from two-thirds of the deposits. Each deposit compounds on its own clock, so the early ones do the most work.
At a glance
$10,000 at 5% a year: simple interest vs. interest compounded annually
| Years | Simple interest | Compound interest | Extra from compounding |
|---|---|---|---|
| 5 | $12,500.00 | $12,762.82 | $262.82 |
| 10 | $15,000.00 | $16,288.95 | $1,288.95 |
| 20 | $20,000.00 | $26,532.98 | $6,532.98 |
| 30 | $25,000.00 | $43,219.42 | $18,219.42 |
| 40 | $30,000.00 | $70,399.89 | $40,399.89 |
Put it in your plan
Compound interest in MoneyWhatIf
MoneyWhatIf compounds every account year by year: each year’s return acts on the balance the previous year closed with. Contributions, withdrawals, required distributions and sweeps are dated mid-year, so each earns or forgoes half a year of that year’s return. Cash accounts carry their own return assumption, and loans calculate interest and principal inside each projected year. Turn on Today’s money to divide compounded future balances by cumulative plan inflation, or use the log scale to keep early balances readable beside much larger later ones.
Common questions
Compound interest FAQs
How do you calculate compound interest?
Multiply the principal by (1 + r ÷ n) raised to the power n × t, where r is the annual rate as a decimal, n the compounding periods per year and t the number of years. For $5,000 at 4% compounded monthly for 15 years: 5,000 × (1 + 0.04 ÷ 12)^180 ≈ $9,101.51, of which about $4,101.51 is interest. For regular deposits, the SEC’s Investor.gov compound interest calculator does the arithmetic and lets you pick the compounding frequency.
Do mortgages use compound interest?
Not while you pay on schedule. A standard amortizing loan, such as most fixed-rate mortgages, charges each month’s interest on the remaining principal and collects it with that month’s payment, so interest is not added to the balance and never earns interest itself. A loan starts compounding against you only when a payment falls short of the interest due and the unpaid interest joins the balance.
Do stocks earn compound interest?
Not interest, strictly, because stocks pay no fixed rate. But reinvested dividends and rising prices compound in the same way, since each year’s return applies to a larger holding. The difference is certainty: a savings account’s rate is known, while stock returns vary and can be negative for years at a time. Describe past growth with a compound annual growth rate rather than an average, and treat any future rate as an assumption.
Does a 401(k) earn compound interest?
A 401(k) holds investments rather than paying a set rate, so it compounds through returns: dividends and interest are reinvested and gains build on earlier gains. Its tax treatment helps. Earnings inside a 401(k) or IRA are not taxed as they occur, so none of the yearly return is lost to tax along the way; pre-tax contributions and earnings in traditional accounts are taxed at withdrawal, and qualified Roth withdrawals are tax-free. Fund fees still compound against the balance.
What is continuous compounding?
Continuous compounding is the limit reached by crediting interest infinitely often, using A = P × e^(r × t), where e is about 2.71828. It caps what frequency can add: at a 5% rate it produces an APY of about 5.13%, the same to two decimals as daily compounding. It appears mostly in financial models rather than on consumer accounts.