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Daily Compound Interest Calculator

Quick answer

A = P(1+r/365)^(365t): 10,000 at 5% compounded daily reaches 11,618 in 3 years — an effective APY of 5.127% versus 5% annual.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How Does the Daily Compound Interest Calculator Work?

A = P × (1 + r ÷ 365)^(365 × t)

Daily compounding credits interest 365 times a year, so each day’s interest earns its own interest tomorrow. The formula divides the nominal annual rate by 365 and raises the base to the power of days elapsed. Example: 10,000 at a 5% nominal rate for 3 years grows to 10,000 × (1 + 0.05/365)^1095 ≈ 11,618.34 — versus 11,576.25 with annual compounding, a free 42.09 purely from frequency. The effective annual rate becomes (1 + 0.05/365)^365 − 1 = 5.127% APY. As frequency increases the gains shrink toward the continuous limit Pe^rt (11,618.94 here), which is why banks quote APY: it makes frequency differences visible. Credit cards run the same math against you — 24% APR compounds daily to about 26.8% effective if you carry balances.

  1. 1

    Step 1

    Enter the principal and the nominal annual rate.

  2. 2

    Step 2

    Enter the time in years (365-day convention is standard).

  3. 3

    Step 3

    Read the final amount and the interest earned.

  4. 4

    Step 4

    Compare with monthly or annual compounding to see the frequency edge.

Use Cases

Savings account comparison

Checking what daily compounding really adds over monthly

CD ladder pricing

Valuing brokered CDs quoted at different compounding bases

Card cost awareness

Seeing the true effective rate behind a daily-compounding APR

Leap-year precision

Handling 366-day years for multi-year deposits

Common Mistakes

  • Confusing nominal rate with APY

  • Expecting huge daily advantage

  • Dividing by the wrong day count

FAQs

What is daily compound interest?

Interest credited every day on a balance that already includes prior interest: A = P(1 + r/365)^(365t). 10,000 at 5% for 3 years becomes ≈11,618.34.

How much more is daily vs annual compounding?

On 10,000 at 5% for 3 years: 11,618.34 versus 11,576.25 — about 42 extra, because each day’s interest starts earning immediately.

What APY does 5% compounded daily equal?

(1 + 0.05/365)^365 − 1 = 5.127% — the effective rate that makes daily products comparable with annual ones.

Is daily compounding the same as continuous?

Nearly: continuous uses Pe^rt and gives 11,618.94 on our example — just 0.60 more than daily. Frequency gains shrink as they approach the limit.

Do credit cards compound daily?

Most do: a 24% APR divided by 365 accrues about 0.0658% per day on balances, compounding to ≈27% effective annually if unpaid — another reason to pay in full.

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Monthly interest = balance × APY ÷ 12: 20,000 at 3.75% earns 62.5 a month — about 763 over a year with monthly compounding.

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Calculate forward exchange rate from interest rate parity.

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Total return = (final − initial) ÷ initial: 20,000 growing to 27,500 in 3 years is +37.5% total, ≈11.2% annualized.

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FV = P(1+r)^t + PMT·((1+r)^t−1)/r: 10,000 plus 250 monthly at 7% grows to ≈75,900 in 15 years — deposits and compounding combined.

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Home loan payment = P × r(1+r)^n/((1+r)^n−1). See the monthly installment, total interest and payoff cost for any house price, rate and term.