Compound Interest Calculator

A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. When you also add money regularly, the future value of those contributions is added: PMT x [((1 + r/n)^(nt) - 1) / (r/n)]. This calculator grows every deposit from its own date, which reproduces that formula — you can check each year in the ledger.

More often is better, but the effect is small next to rate and time. At 7%, annual compounding yields 7.00% effective, monthly 7.23% and daily 7.25%. On $10,000 at 5% for one year, daily compounding earns $1.05 more than monthly. An account paying a rate 0.25 points higher matters far more than the compounding schedule.

APR is the nominal annual rate before compounding. APY (annual percentage yield) is what you earn once compounding is applied: APY = (1 + r/n)^n - 1, the figure US banks must disclose on deposit accounts under Regulation DD. Compare savings accounts on APY: 6.00% compounded monthly is a 6.168% APY, so it beats a 6.10% APY but loses to 6.20%.

The Rule of 72 gives a quick estimate: divide 72 by the annual return. At 6% doubling takes about 72 / 6 = 12 years; at 9% about 8 years. The exact time is ln(2) / ln(1 + r) — 11.9 years at 6% — so the rule is within a few months for rates between about 5% and 12%. The annual ledger shows the year your balance passes double what you put in.

Each deposit compounds from the day it is made, so regular contributions grow on their own curve. At 7% over 30 years, a $10,000 starting balance alone grows to $81,165; adding $200 a month takes it to $325,159 — about $244,000 more, of which $72,000 is the deposits themselves. The composition bar under the result shows the split between starting amount, contributions and growth.

Simple interest is paid only on the original principal: interest = P x r x t. Compound interest is paid on the principal plus all interest already credited, so the balance grows exponentially. Over 20 years at 7%, $10,000 grows to $24,000 with simple interest, $38,697 compounded annually and $40,387 compounded monthly — $16,387 more than simple interest.

Yes — on debt. A credit card compounds interest on the unpaid balance, usually daily. A $5,000 balance at 20% APR with no payments grows to about $6,107 after one year and $13,588 after five (set compounding to Daily and contributions to 0 to reproduce it). Compounding works for you on savings and against you on debt, at whatever rate applies.

It models an advisory fee or fund expense ratio. The fee is subtracted from the annual return before compounding, so a 7% return with a 0.5% fee compounds at 6.5%. Over 30 years, $50,000 grows to $405,825 at 7% and $349,590 at 6.5% — the half-point fee costs about $56,000. The net rate and its APY appear in the KPI cells under the result.

Enter an inflation rate under Advanced assumptions and the calculator divides the nominal balance by (1 + inflation)^years, converting future dollars into today's purchasing power. The Federal Reserve's longer-run inflation goal is 2%; the page defaults to 2.5%. The adjustment does not change the nominal projection; it adds the "After inflation" figure, ledger column and chart line.

At a 7% average annual return compounded monthly, $500 a month grows to about $609,986 after 30 years. You contribute $180,000 of that; the other $429,986 is growth. At 10% the same deposits reach about $1.13 million, and at 4% about $347,025 — long projections are very sensitive to the rate assumed. These are nominal figures before fees, taxes and inflation.

Far more than the extra deposits. Saving $200 a month at 7% for 30 years produces about $243,994; the same $200 a month for 40 years produces about $524,963. The extra decade adds $24,000 of contributions but roughly $281,000 of ending balance, because the earliest deposits have the longest time to compound.

It depends on the account. Interest from a savings account, CD or taxable brokerage account is generally taxable in the year it is credited, whether or not you withdraw it; the payer reports it on Form 1099-INT when it is $10 or more. In a traditional 401(k) or IRA growth is tax-deferred until withdrawal, and qualified Roth withdrawals are tax-free. Check IRS Topic 403 for the current rules.