Compound Interest Calculator

Use the Compound Interest Calculator shown below to compare or translate interest rates across various compounding intervals. For performing real compound‑interest computations, head over to our Interest Calculator.

What is compound interest?

Interest represents the price paid for borrowing funds, essentially the compensation a lender gets for providing money to a borrower. Typically, the borrower pays a fraction of the principal as interest. Interest can be classified as either simple or compound.

Simple interest is calculated solely on the original principal, typically expressed as a fixed percentage. To compute the interest due, multiply the principal by the rate and by the number of periods the loan is outstanding. For instance, borrowing $100 at a 10 % yearly simple rate for two years would generate interest equal to:

$100 × 10% × 2 years = $20

In practice, simple interest is uncommon; compound interest dominates. With compound interest, earnings accrue on the original principal as well as on previously earned interest. As an illustration, borrowing $100 at a 10 % annual compound rate would produce interest of the following amount after the first year:

$100 × 10% × 1 year = $10

At the end of the first year, the loan's balance is principal plus interest, or $100 + $10, which equals $110. The compound interest of the second year is calculated based on the balance of $110 instead of the principal of $100. Thus, the interest of the second year would come out to:

$110 × 10% × 1 year = $11

The total compound interest after 2 years is $10 + $11 = $21 versus $20 for the simple interest.

Since lenders receive interest on previously accumulated interest, the returns expand over time much like a snowball gaining mass exponentially. Consequently, compound interest can provide substantial financial gains for lenders, and the longer the compounding period, the larger the increase.

As a simple example, a young man at age 20 invested $1,000 into the stock market at a 10% annual return rate, the S&P 500's average rate of return since the 1920s. At the age of 65, when he retires, the fund will grow to $72,890, or approximately 73 times the initial investment!

Although compound interest is a powerful tool for building assets, it can be detrimental to borrowers. In this sense, it acts as a double‑edged sword: delaying repayment or extending a debt can cause the total interest obligation to rise sharply.

Different compounding frequencies

Interest may be compounded at various intervals, though annual and monthly schedules are most common. The chosen frequency influences the amount due. For example, a loan quoted at 10 % with semi‑annual compounding effectively applies a 5 % rate each half‑year. On a $100 loan, the interest accrued in the first six months would be:

$100 × 5% = $5

For the second half of the year, the interest rises to:

($100 + $5) × 5% = $5.25

The total interest is $5 + $5.25 = $10.25. Therefore, a 10% interest rate compounding semi-annually is equivalent to a 10.25% interest rate compounding annually.

Savings accounts and certificates of deposit generally compound interest once a year, whereas mortgages, home‑equity loans, and credit cards typically use monthly compounding. Frequently compounded rates often look smaller, which is why lenders prefer to quote monthly rates. For instance, a 6 % mortgage translates to a 0.5 % monthly rate, but when that monthly rate is compounded, the effective annual yield rises to about 6.17 %.

Our compound interest calculator above accommodates the conversion between daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous (meaning an infinite number of periods) compounding frequencies.

Compound interest formulas

Computing compound interest may require complex equations. Our tool streamlines the process, but if you wish to explore the underlying mathematics, the formulas are listed below:

Basic compound interest

The basic formula for compound interest is as follows:

A_t = A₀(1 + r)ⁿ

Consider this scenario: a saver deposits $1,000 into an account that provides a 6 % APY, compounded annually for two years. Apply the earlier formula to determine the amount that will be available at maturity:

A_t = $1,000 × (1 + 6%)² = $1,123.60

For other compounding frequencies (such as monthly, weekly, or daily), prospective depositors should refer to the formula below.

Imagine the $1,000 deposited in the earlier savings‑account scenario earns a 6 % annual rate that is compounded each day. That translates to a daily rate of:

6% ÷ 365 = 0.0164384%

Using the formula above, depositors can apply that daily interest rate to calculate the following total account value after two years:

A_t = $1,000 × (1 + 0.0164384%)^{(365 × 2)}

A_t = $1,000 × 1.12749

A_t = $1,127.49

Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.

Continuous compound interest

When interest compounds continuously, it approaches the theoretical maximum that compound interest can achieve over a given timeframe. The formula for continuous compounding is shown below:

A_t = A₀e^rt

For instance, we wanted to find the maximum amount of interest that we could earn on a $1,000 savings account in two years.

Using the equation above:

A_t = $1,000e^{(6% × 2)}

A_t = $1,000e^0.12

A_t = $1,127.50

The examples illustrate that more frequent compounding boosts the amount of interest earned. Yet, once the compounding interval becomes very short, the incremental benefit for most savers diminishes, especially on modest principal sums.

Rule of 72

The Rule of 72 offers a quick way to estimate how many years it will take for an investment to double when a steady, annually‑compounded return is applied. Divide 72 by the annual percentage yield to get the approximate doubling period.

Take a $100 investment that yields a fixed 8 % return each year. Using the Rule of 72, 72 ÷ 8 ≈ 9, so the money will roughly double in nine years. Remember, the figure \"8\" represents 8 %, not 0.08, and the rule provides only a rough guide, not a precise calculation.

History of Compound Interest

Archaeological records show that the Babylonians and Sumerians were already experimenting with compound interest around 4,400 years ago. Their method differed from modern practice: they let the interest grow to equal the original principal and then added that amount back to the principal.

In many ancient legal systems, simple interest was accepted, while compound interest was often condemned as usury. Roman law, as well as Christian and Islamic teachings, denounced it as immoral. Despite such restrictions, lenders employed compound interest throughout the Middle Ages, and its use expanded after the 1600s when compound‑interest tables were published.

Another factor that popularized compound interest was Euler's Constant, or "e." Mathematicians define e as the mathematical limit that compound interest can reach.

While studying compound interest in 1683, Jacob Bernoulli discovered the constant e. He realized that increasing the number of compounding periods within a fixed time span accelerates growth, regardless of whether the intervals are measured in years, months, or days. Each extra period yields a higher return, and the series converges toward the limit e, which links the growth factor to the interest rate.

Leonhard Euler later discovered that the constant equaled approximately 2.71828 and named it e. For this reason, the constant bears Euler's name.