Compound Interest Calculator (Daily, Monthly & Yearly Compounded)

Online Compound Interest Calculator

Use the compound interest calculator below to quickly calculate the compound interest and total future value of your investment based on the initial principal amount. You can also include additional contributions and choose from daily, monthly, quarterly, semiannual, or annual compounding periods. The calculator updates instantly, giving you real-time results as soon as you enter your details.

Definition: A compound interest calculator is a simple tool that helps you estimate how your money grows over time by adding interest on both the original amount and the interest already earned.

What Is Compound Interest?

Compound interest is interest calculated on the initial principal plus on any accumulated interest from prior periods. It is common in savings accounts, certificates of deposit, and many investment vehicles. The key idea is reinvestment. When you reinvest interest, it becomes part of the new principal and produces additional interest in subsequent periods.

Compound interest is sometimes called “interest on interest.” It is a powerful concept in personal finance because compounding can make modest contributions grow substantially over time.

How Compound Interest Works

Compound interest operates across a series of repeating cycles. Each cycle is one compounding period. The frequency of those cycles matters. Common compounding frequencies include daily, monthly, quarterly, semiannual, and annual. The technical mechanics are straightforward.

1. Start with the principal. This is the original deposit.
2. For each compounding period, calculate interest by applying the periodic rate to the current balance.
3. Add the interest to the balance.
4. Repeat for the total number of periods that correspond to the time horizon.

Two mathematical pieces drive the behavior. One is the periodic interest rate, which is the annual interest rate divided by the number of compounding periods per year. The second is the total number of compounding periods, which equals the number of years multiplied by the number of compounding periods per year.

If interest compounds more frequently, the periodic rate is smaller, but the number of periods is larger. The net result is typically a higher effective annual return when compounding frequency increases.

How to Use The Compound Interest Calculator

Our Compound Interest Calculator is designed to be user-friendly and to return instant results display when you click the Calculate button. Follow these steps to use it efficiently.

1. Enter the initial investment or current principal in the first field.
2. Enter the time duration and choose the unit for that duration. Options include years, half-years, quarters, months, and days.
3. Enter the annual interest rate as a percentage in the interest rate field.
4. Select a compounding frequency. The calculator supports daily, monthly, quarterly, semiannual, and annual compounding.
5. Optionally, enter a contribution amount to be added at regular intervals. Choose the contribution frequency to match your deposit schedule, such as yearly, monthly, or daily.
6. Select whether contributions are added at the start of each period or at the end of each period.
7. Click the Calculate button. The results will appear instantly below the form — there is no page reload.

Use the instant feedback to try different contribution amounts, compounding frequencies, and time horizons. This helps you see how small differences change long-term outcomes.

Compound Interest Formula

The core formula for compound interest when contributions are not present is:

Where:

• P is the principal or initial deposit.
• r is the annual nominal interest rate, expressed as a decimal.
• n is the number of compounding periods per year.
• t is the time in years.
• A is the final amount after t years.

When you add regular contributions, a common approach is to compute the future value of an annuity and add that to the compounded principal. The calculator uses a practical implementation that converts contribution frequency to the compounding frequency and applies the appropriate annuity formula. This yields a realistic future value for typical deposit schedules.

Compound Interest Example Calculations

This section walks through a few example scenarios so you can see compound interest in action.

Example 1: No contributions, yearly compounding

1. Principal: 10,000
2. Annual rate: 2 percent
3. Compounding: once per year
4. Time: 3 years

Calculation outline

1. Periodic rate (r ÷ n) = 0.02
2. Number of periods (n × t) = 3
3. Future value: A = 10,000 × (1.02)³ = 10,612.08

Result summary: Value after 3 years = 10,612.08. Interest accrued = 612.08. Capital growth = 6.121 percent.

Example 2: Monthly contributions, monthly compounding

1. Principal: 5,000
2. Annual rate: 5 percent
3. Contribution: 100 per month, added at the end of each month
4. Compounding: monthly for 10 years

Calculation outline

1. Convert annual rate to monthly periodic rate: 0.05 ÷ 12
2. Compute the future value of the principal compounded monthly.
3. Compute the future value of the monthly contributions using the annuity formula.
4. Sum both results.

Result summary: You will see the final amount and the portion that came from interest. Try these inputs in the calculator to get instant results display and test sensitivity to a different contribution amount or to contributing at the start of each period.

These two scenarios show how compounding and contributions combine. When contributions are frequent and sustained, the contribution stream can outweigh the initial principal as the primary driver of growth.

Compound Interest versus Simple Interest

Understanding the difference is essential.

Simple interest is calculated only on the principal. The interest amount for each period is constant and does not compound. The formula is straightforward:

Interest = Principal × Rate × Time

Compound interest uses the principal plus accumulated interest. Each period, the interest amount is recalculated on the new balance. Over the same nominal rate and time, the compound interest outcome is greater than or equal to the simple interest outcome. The advantage of compounding grows with higher rates and longer time horizons.

Practical implications:

1. For short-term, low rates, the difference may be small.
2. For long-term, higher rates, the accumulated difference can be substantial.
3. Choosing frequent compounding increases the effective return compared with annual compounding, given the same nominal rate.

Factors That Influence Compound Interest

Several variables determine how quickly your investment grows.

1. Principal amount: The larger the starting balance, the more absolute interest you earn each period. Compound interest amplifies the effect of a larger principal.
2. Interest rate: The nominal annual rate is the most direct lever. Small changes in the rate can produce large differences over many years.
3. Time horizon: Time is a powerful multiplier. The longer you leave your money invested, the more periods interest has to compound.
4. Compounding frequency: More frequent compounding increases the effective annual rate for the same nominal rate. Daily, monthly, or quarterly compounding yields higher final values than annual compounding, all else equal.
5. Contributions and withdrawals: Regular contributions increase the base that compounds. Regular withdrawals reduce the compounding base. The timing of contributions — at the start or at the end of each period — also matters.
6. Taxes and fees: Real-world returns are affected by taxes and account fees. These are not included in the basic compound interest formula but significantly affect net outcomes. Account selection and tax planning matter.

How Often Interest Is Compounded

Common compounding schedules include the following:

1. Daily compounding: Interest is calculated every day. This is common in some savings accounts.
2. Monthly compounding: Typical for many bank accounts and investment calculations.
3. Quarterly compounding: Splits the year into four periods.
4. Semiannual compounding: Uses two periods per year.
5. Annual compounding: A single compounding event per year.

The effective annual rate equals one plus the periodic rate raised to the number of periods per year, minus one. Increasing the frequency of compounding increases the effective annual rate while keeping the nominal rate unchanged.

How to Calculate Compound Interest Manually

If you want to compute compound interest without a calculator, follow these steps.

1. Convert the annual rate from percent to decimal by dividing by one hundred. For a 5 percent rate, r = 0.05.
2. Determine the number of compounding periods per year (n). For monthly, n = 12; for daily, n = 365, and so on.
3. Determine the total number of periods (N) by multiplying n by the number of years (t).
4. Compute the periodic rate: i = r ÷ n.
5. Calculate the future value of the principal using the formula A = P × (1 + i)ᴺ.
6. If you have regular contributions, compute the future value of the contribution stream using the annuity future value formula, then add that to A.
7. Subtract the original principal and total contributions to find the interest accrued.

Manual calculation is precise but can become tedious for frequent contributions and irregular schedules. Use the Compound Interest Calculator to produce instant results display and to avoid manual arithmetic.

FAQs About Compound Interest

Q1: Can my account compound more than once per day?
A1: Most financial institutions limit compounding to daily at most. Check account disclosures for the specific compounding policy.

Q2: Does the calculator include taxes and fees?
A2: No, the calculator computes pre-tax, gross results. Deduct taxes and fees from the final amount to estimate net proceeds.

Q3: What does “effective interest rate” mean?
A3: The effective interest rate is the actual annual rate earned after accounting for compounding. It is higher than the nominal rate when compounding occurs more than once per year.

Q4: How should I choose contribution frequency?
A4: Choose the contribution frequency that matches how often you will actually deposit funds. That makes results realistic. The calculator supports yearly, half-yearly, quarterly, monthly, and daily frequencies.

Q5: Can contributions be negative for withdrawals?
A5: Yes, you can enter negative contribution values to model regular withdrawals. The calculator acknowledges contributions entered as negative numbers.

Q6: What is the benefit of compounding at the start of a period?
A6: Contributions at the start of each period have more time to compound within that period and therefore yield slightly higher final values than contributions at the end of each period.

Q7: How accurate are the results?
A7: The results follow classic compound interest formulas and include a pragmatic approach to contributions. For complex, tax-adjusted, or variable-rate scenarios, consult a financial planner or run scenario tests.

Final Guidance and Best Practices

1. Start early. Time is the most powerful force in compound interest.
2. Increase contributions gradually. Small recurring contributions often have outsized, long-term impact.
3. Compare compounding frequency across accounts. A higher effective rate yields more growth over time.
4. Watch fees and taxes. They reduce net returns and can erode compounding benefits.
5. Use this tool to experiment. Because the calculator provides instant results display, you can try many combinations quickly and discover realistic savings and investment paths.

This guide explains how compound interest works, why it matters, and how to use the Compound Interest Calculator to model realistic deposit scenarios. Use the instant results display to compare options, test assumptions, and plan with confidence.