Compound Interest Calculator

What is compound interest?

Compound interest is interest earned on both your original money and the interest that has already accumulated. That means your balance can grow faster over time because each period begins with a larger amount.

Compound interest formula

In this formula, A is the final balance, P is the initial principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the time in years. Recurring contributions are calculated separately and added after growing for the time remaining after each end-of-period deposit.

How compounding frequency works

Daily compounding applies interest 365 times per year, while monthly, quarterly, semiannual, and annual compounding apply it 12, 4, 2, and 1 time per year. With the same stated annual rate, more frequent compounding usually produces a slightly higher balance because interest begins earning interest sooner.

Compound vs. simple interest

Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus accumulated interest, so the difference becomes more noticeable with higher rates, longer time periods, and more frequent compounding.

How recurring contributions affect growth

Regular deposits increase both the money you put in and the amount that can earn interest. This calculator assumes each contribution is made at the end of its contribution period. When contribution and compounding frequencies differ, every deposit is grown for its own remaining time instead of using a same-frequency shortcut.

Worked example

A $1,000 initial investment earning 5% annually for 10 years with annual compounding and no further contributions grows to about $1,628.89. The $628.89 difference is interest earned on the original principal and accumulated interest.

Frequently asked questions

How the compound interest calculator works

Start with the amount you have today, the annual interest rate, and how many years the money will stay invested. Then pick how often interest is compounded: daily (365 times a year), monthly, quarterly, semiannually, or annually. If you plan to keep adding money, enter a recurring contribution and how often you make it. The contribution schedule does not have to match the compounding schedule; you can add $200 a month to an account that compounds daily.

The calculator grows the initial deposit with the standard compound interest formula and grows each contribution separately for the time it remains invested, assuming every deposit lands at the end of its period. It reports the final balance, the initial principal, the total of all contributions, the total interest earned, and the number of deposits made. Below the results, a year-by-year table shows the balance at the end of each year for up to 50 years.

Compound interest formulas

A is the final balance, P is the starting principal, r is the annual rate as a decimal, n is the number of compounding periods per year, t is the time in years, and C is the contribution made at the end of each period. The contribution formula shown is the simplified version that applies when you contribute and compound at the same frequency. When the two differ, the calculator values each deposit individually rather than using this shortcut.

Suppose you deposit $5,000 at 6% compounded monthly for 10 years. The monthly rate is 0.06 ÷ 12 = 0.005, and there are 120 periods, so the growth factor is 1.005^120 = 1.8194. The balance becomes 5,000 × 1.8194 = $9,096.98, of which $4,096.98 is interest. Add a $200 deposit at the end of every month and the contributions alone grow to 200 × (1.8194 − 1) ÷ 0.005 = $32,775.87. The final balance is $41,872.85: $5,000 of principal, $24,000 of contributions, and $12,872.85 of interest.

Why compounding frequency matters

At the same stated rate, more frequent compounding produces a slightly higher balance because interest starts earning interest sooner. The effect is real but smaller than most people expect. Using the same $5,000 at 6% for 10 years with no contributions, annual compounding gives $8,954.24, monthly compounding gives $9,096.98, and daily compounding gives $9,110.14. Moving from monthly to daily adds about $13 over a decade.

Banks express this difference as the annual percentage yield (APY), which is the effective rate after compounding. A 6% rate compounded monthly has an APY of about 6.17%. If the account you are modeling quotes an APY rather than a rate, choose annual compounding and enter the APY directly; the result will match.

What the calculator is useful for

Compound growth is the same math whether the money sits in a bank or in an investment account, so the tool works for any scenario with a steady rate of return. Common uses include:

• Estimating what a high-yield savings account or certificate of deposit will be worth at maturity
• Projecting a retirement or brokerage account using an assumed average annual return
• Comparing two offers by changing only the rate or the compounding frequency
• Seeing how much of a long-term balance comes from contributions versus interest
• Testing how starting five years earlier, or adding $50 a month, changes the outcome

Assumptions and limitations

The rate you enter is applied unchanged for the whole period. Savings rates move with the market, and investment returns vary from year to year, so treat long-range projections as an illustration rather than a forecast. The calculator also ignores taxes on interest, account fees, and inflation, each of which reduces what the final balance will actually buy.

Contributions are counted at the end of each period, which is the usual convention for paycheck deposits and matches how most banks credit interest. The number of deposits is the whole number of contribution periods that fit in the time you entered, so 10.5 years of monthly deposits counts 126 payments. Entering a 0% rate is allowed and simply sums the principal and deposits.

Frequently asked questions

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