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Daily Compound Interest Calculator

Enter the principal, annual rate, and years to find the daily-compounded growth.

Result

$11,618.22
$1,618.22
5.13%

How it is calculated

The nominal annual rate is split into 365 equal daily rates and applied for every day of the term: FV = principal × (1 + rate ÷ 100 ÷ 365)365 × years. Interest is FV − principal. The tool also reports the effective annual yield, APY = ((1 + rate ÷ 100 ÷ 365)365 − 1) × 100, which is what one year of daily compounding really pays. The rate field is the nominal rate (APR), not an APY, and the year is always 365 days with no leap day. Years can be fractional (0.5 is half a year). A rate or principal of zero is accepted and simply returns the principal with no interest. A negative rate, principal or term gives no result, and neither does a term so long that the number overflows. The figure is before tax and assumes the rate never changes and nothing is added or withdrawn.

Worked example

Deposit 10000 at a nominal 5% a year for 3 years. Step 1: daily rate = 5 ÷ 100 ÷ 365 = 0.013699%. Step 2: number of days = 365 × 3 = 1095. Step 3: growth factor = (1.00013699)1095 = 1.161822. Step 4: future value = 10000 × 1.161822 = $11,618.22. Step 5: interest = $1,618.22. One year alone yields an effective APY of 5.13%, a little above the stated 5%, because each day's interest earns interest the next day.

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Common mistakes

  • Entering an APY in the rate field. The tool applies daily compounding to the number you give, so an APY entered here is compounded a second time and overstates growth. Use the nominal rate.
  • Expecting a big gain from daily over monthly compounding. At 5% the effective yield is 5.13% versus about 5.12% monthly, so the rate and term matter far more.
  • Entering months as years. Six months is 0.5, not 6.
  • Typing the rate as 0.05 instead of 5. The field is in percent.
  • Forgetting that no deposits or withdrawals are modelled. Regular additions need a different tool, and tax on the interest is also left out.

Sources

About this calculator

Daily compounding calculates interest on a balance every single day rather than monthly, quarterly, or annually, with each day’s interest added to the principal so the next day’s interest is earned on a slightly larger base. The formula is A = P(1 + r/365)^(365×t), where P is the principal, r is the annual interest rate, and t is the time in years — 365 replaces the usual compounding-periods-per-year figure used for other frequencies.

Because interest gets added to the balance more frequently, daily compounding produces a very slightly higher effective return than the same nominal rate compounded monthly or annually — the difference is small but real, and it’s why the Annual Percentage Yield (APY) disclosed by high-yield savings accounts and some credit card issuers is calculated after accounting for compounding frequency, not just the stated nominal rate.

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