How do you calculate compound interest?

Use A = P(1 + r/n)^(nt). For $2,000 at 5% compounded quarterly for 3 years: r/n = 0.0125 and nt = 12, so A = 2,000 × 1.0125^12 = 2,000 × 1.16075 = $2,321.51. The interest is A − P = $321.51.

What is the difference between APR and APY?

The APR (or nominal rate) is the rate before compounding; the APY is what you actually earn in a year once compounding is included. 6% compounded monthly is an APY of 6.168%. The page shows the APY for whatever compounding you choose.

How often is interest compounded on a savings account?

Usually daily, and credited monthly — check the account's terms. Daily and monthly compounding differ very little: 10,000 at 6% for 10 years gives 18,220 with daily compounding and 18,194 with monthly.

What is the rule of 72?

A shortcut for doubling time: divide 72 by the annual rate. At 8%, money doubles in about 72 ÷ 8 = 9 years; the exact figure with monthly compounding is 8.7 years. It works best for rates between about 4% and 12%.

Is compound interest always better than simple interest?

For a saver, yes — for the same principal, rate and period, compound interest always meets or exceeds simple interest because each period's interest is added to the base. The gap is small over short periods and large over decades. For a borrower, the same effect works against you.

Compound Interest Calculator (Daily, Monthly, Quarterly or Annual)

Future value of a lump sum with compounding annually, quarterly, monthly, daily or continuously — with the APY, doubling time and a year-by-year table.

Inputs

CurrencyAuto (USD)

Principal

$10$515,500

Annual rate(%)

0 %30 %

Years(years)

1 years50 years

Compounding

Include CalculateEveryday mark

Future value

$22,196

Future value

Principal$10,000(45%)
Interest$12,196(55%)

Growth year by year

Year	Balance	Interest so far
1	$10,830	$830
2	$11,729	$1,729
3	$12,702	$2,702
4	$13,757	$3,757
5	$14,898	$4,898
6	$16,135	$6,135
7	$17,474	$7,474
8	$18,925	$8,925
9	$20,495	$10,495
10	$22,196	$12,196

Interest earned: $12,196
Principal: $10,000
Compounding: Monthly
Working: (1 + 0.08 ÷ 12)^(12 × 10) = 2.21964 — the principal grows by that factor
Effective annual rate (APY): 8.3%
Simple interest would give: $18,000
Doubling time: 8.7 years (rule of 72: 9.0)

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What each Compound Interest input means

Principal: The amount you start with. It is invested once; this page adds no further deposits.
Annual rate: The nominal annual rate before compounding — the 'interest rate', not the APY. If you only know the APY, enter it with annual compounding.
Years: How long the money stays invested.
Compounding: How often interest is added: annually (1), semiannually (2), quarterly (4), monthly (12), daily (365) or continuously. Check the account terms.

Compound Interest formula

A = P × (1 + r/n)^(n × t) · continuous: A = P × e^(r × t) · APY = (1 + r/n)^n − 1

A = P \left(1 + \dfrac{r}{n}\right)^{n t}

Compound interest is interest on interest: each period's interest is added to the balance, and the next period's interest is charged on the larger amount. OpenStax's Contemporary Mathematics gives the formula used here: A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the number of times a year interest is added and t the number of years. Choose the compounding to match the account — banks often compound daily or monthly, bonds semiannually, and textbook problems annually; 'continuously' is the limit as n grows without end, A = Pe^(rt). More frequent compounding earns a little more on the same nominal rate, and the page shows that as the effective annual rate, which US banks must disclose as the APY under the Truth in Savings rule. It also shows what simple interest would have paid, the time to double your money (with the rule of 72 beside it) and the balance at the end of each year. For regular deposits on top of a lump sum, use the investment or SIP calculators.

Compound Interest worked example

$10,000 at 8% compounded monthly for 10 years: (1 + 0.08 ÷ 12)^120 = 2.2196, so it grows to about $22,196 — $12,196 of interest. Monthly compounding turns 8% into an effective 8.3% a year. Simple interest would have reached only $18,000, and the money doubles in about 8.7 years (the rule of 72 says 9).

More Compound Interest examples

$5,000 in a savings account paying 4.5% compounded daily for 5 years becomes $6,262. Daily compounding makes the APY 4.602%, so the account earns about $137 more than simple interest's $6,125.

$1,000 at 6% compounded once a year for 20 years: 1.06^20 = 3.2071, so it grows to $3,207. Simple interest would give $2,200; the extra $1,007 is interest earned on earlier interest.

Where the Compound Interest calculator can give the wrong answer

The rate is held constant for the whole period. Savings rates change, and investment returns vary from year to year; a fixed rate is a planning assumption.
Tax on the interest is not deducted. In a taxable account each year's tax reduces what compounds, so the real result is lower.
A 0% rate correctly returns the principal unchanged. Negative rates are refused.
Banks that compound daily may use a 360- or 365-day year, which changes the result by a few cents on typical balances.
This models a single lump sum with no further contributions or withdrawals — adding regular deposits is what the investment and SIP calculators are for.

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Compound Interest reference table

What 10,000 at 6% becomes after 10 years, by compounding
Compounding	Periods a year	Value after 10 years	Effective annual rate
Annually	1	17,908	6.000%
Quarterly	4	18,140	6.136%
Monthly	12	18,194	6.168%
Daily	365	18,220	6.183%
Continuously	∞	18,221	6.184%

Source: Computed with A = P(1 + r/n)^(nt) and A = Pe^(rt) (OpenStax §6.4)

Compound Interest FAQ

: Use A = P(1 + r/n)^(nt). For $2,000 at 5% compounded quarterly for 3 years: r/n = 0.0125 and nt = 12, so A = 2,000 × 1.0125^12 = 2,000 × 1.16075 = $2,321.51. The interest is A − P = $321.51.
: The APR (or nominal rate) is the rate before compounding; the APY is what you actually earn in a year once compounding is included. 6% compounded monthly is an APY of 6.168%. The page shows the APY for whatever compounding you choose.
: Usually daily, and credited monthly — check the account's terms. Daily and monthly compounding differ very little: 10,000 at 6% for 10 years gives 18,220 with daily compounding and 18,194 with monthly.
: A shortcut for doubling time: divide 72 by the annual rate. At 8%, money doubles in about 72 ÷ 8 = 9 years; the exact figure with monthly compounding is 8.7 years. It works best for rates between about 4% and 12%.
: For a saver, yes — for the same principal, rate and period, compound interest always meets or exceeds simple interest because each period's interest is added to the base. The gap is small over short periods and large over decades. For a borrower, the same effect works against you.