Visualize Exponential Growth
Demonstrates how interest begins earning interest on itself, turning modest initial balances into substantial sums over multi-year holding periods.
Compound Interest Calculator
Free compound interest calculator to forecast investment growth, interest earned, and ending balance with periodic deposits and flexible compounding frequency.
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Compound Interest & APY Formulas
Last reviewed: September 2026Calculation Formula
Compound Interest: A = P × (1 + r/n)^(n×t)
Simple Interest: A = P × (1 + r×t)
Annual Percentage Yield (APY) = (1 + r/n)^n - 1
Variables & Definitions
- A:
- Final accrued balance (principal + cumulative interest)
- P:
- Initial principal deposit amount
- r:
- Annual nominal interest rate (as a decimal)
- n:
- Compounding frequency per year (365 = daily, 12 = monthly, 4 = quarterly, 1 = annually)
- t:
- Time duration in years
- APY:
- Effective annual percentage yield including compounding effect
Core Assumptions
- Constant fixed annual interest rate throughout the holding term.
- Interest earned is fully reinvested and added to the principal balance at each compounding period.
- Zero partial withdrawals or early termination penalty fees during the term.
- Calculations apply to fixed deposits, high-yield savings (HYSA), and certificates of deposit (CDs).
Disclaimer: Calculations are mathematical projections for financial education and planning. Variable-rate savings accounts (HYSA) fluctuate based on Federal Reserve benchmark rates. Projections do not account for income taxes on interest earnings (IRS Form 1099-INT) or inflation loss. Consult your banking institution for specific account terms.
Worked Example: $20,000 High-Yield Savings at 5.0% APY Compounded Daily (5 Years)
A saver deposits $20,000 into a high-yield savings account earning a 5.00% APY (compounded daily at a nominal 4.879% rate) with zero additional deposits over a 5-year period:
| Initial Principal Deposit | $20,000.00 |
| Year 1 Ending Balance ($1,000 interest) | $21,000.00 |
| Year 3 Ending Balance | $23,152.50 |
| Total Compound Interest Earned (5 Years) | $5,601.70 |
| Final Account Value | $25,601.70 |
💡 Because interest is credited daily, the saver earns $5,601.70 in total interest — over $720 more than simple interest would generate ($4,879) — proving the accelerating advantage of compound interest over multi-year periods.
How to use Compound Interest Calculator
- 1
Enter your starting principal (initial deposit or cash savings balance).
- 2
Input your annual interest rate and select your compounding frequency (daily, monthly, quarterly, semi-annually, or annually).
- 3
Set your investment or deposit duration in years or months.
- 4
View your future account balance, total compound interest generated, effective APY, and year-by-year accumulation chart.
Why use this tool?
Full Compounding Frequency Support
Supports daily, monthly, quarterly, semi-annual, and annual compounding frequencies to match HYSAs, Treasury bonds, and bank CDs.
APY vs APR Translation
Accurately converts nominal interest rates into true Annual Percentage Yield (APY) so you can directly compare competitive bank offers.
Continue your workflow
Planning to add regular monthly savings deposits alongside compound growth? Use the Project regular monthly investment contributions.
Evaluate whether your high-yield savings rate outpaces historical inflation with the Calculate real purchasing power of interest.
Deciding whether to save or pay off credit card or auto debt? Check the Compare savings interest vs debt interest cost.
Frequently asked questions
What is the difference between compound and simple interest?
Simple interest is calculated solely on your original principal deposit. Compound interest is calculated on your initial principal PLUS all previously accumulated interest. Over long periods, compound interest grows exponentially, while simple interest only grows linearly.
What is the Rule of 72 and how do I use it?
The Rule of 72 is a quick mental math shortcut to estimate how many years it will take for your money to double at a given compound interest rate. Simply divide 72 by your annual interest rate. For example, at a 6% annual return, your money doubles in approximately 72 ÷ 6 = 12 years; at 8%, it doubles in approximately 9 years.
How does daily compounding compare to monthly or annual compounding?
More frequent compounding increases your effective annual return (APY). For example, a $10,000 deposit at 5% nominal rate produces $500.00 in interest with annual compounding, $511.62 with monthly compounding, and $512.67 with daily compounding. While the percentage difference is modest over one year, it compounds into thousands of dollars over decades.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the simple nominal rate over a year without taking compounding into account. APY (Annual Percentage Yield) reflects the true total interest you earn or pay over a full year, incorporating the effect of compounding. APY is always greater than or equal to APR.
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