finance ToolUpdated 2026-09-20

Cumulative & Daily Compound Interest Calculator

High-yield savings accounts, money market funds, and certificates of deposit compound interest daily. Calculate your cumulative returns and effective annual percentage yield (APY) over any time horizon.

Formula & Mathematical Methodology

A = P(1 + r ÷ 365)ⁿ; Cumulative Interest = A - P; APY = (1 + r ÷ 365)³⁶⁵ - 1

Daily compounding calculates daily interest by dividing the nominal annual rate by 365. Each day’s earned interest is added to the principal balance, generating interest upon interest for subsequent days.

Step-by-Step Worked Example

Scenario: $15,000 at 5.25% annual interest compounded daily for 365 days.

1. Daily rate: 5.25% ÷ 365 = 0.0143836% per day.

2. Compounding factor: (1 + 0.000143836)^365 = 1.053899.

3. Final Balance: $15,000 × 1.053899 = $15,808.48.

4. Total Cumulative Interest Earned: $808.48.

5. Effective APY: 5.39% (compared to 5.25% simple rate).

Final Calculated Result: $808.48 Cumulative Interest ($15,808.48 Balance)

Frequently Asked Questions

Why does daily compounding yield more than monthly compounding?

Because interest is reinvested every 24 hours rather than every 30 days, your capital begins generating secondary returns faster, boosting your effective APY.