Compound Interest Calculator
Compare or convert interest rates of different compounding periods
Compound Interest Calculator
Modify the values and click the calculate button to use
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Annual Growth Table
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What is Compound Interest?
Interest is the cost of using borrowed money, or more specifically, the amount a lender receives for advancing money to a borrower. When paying interest, the borrower will mostly pay a percentage of the principal (the borrowed amount). The concept of interest can be categorized into simple interest or compound interest.
Simple Interest vs. Compound Interest
Simple interest refers to interest earned only on the principal, usually denoted as a specified percentage of the principal. To determine an interest payment, simply multiply principal by the interest rate and the number of periods for which the loan remains active.
Example: If one person borrowed $100 from a bank at a simple interest rate of 10% per year for two years, at the end of the two years, the interest would come out to:
$100 × 10% × 2 years = $20
Compound interest is interest earned on both the principal and on the accumulated interest. Compound interest is widely used in the real world because it more accurately reflects how investments grow over time.
Example: If one person borrowed $100 from a bank at a compound interest rate of 10% per year for two years:
Year 1: $100 × 10% = $10 (New balance: $110)
Year 2: $110 × 10% = $11 (Total interest: $21 vs $20 for simple interest)
Because lenders earn interest on interest, earnings compound over time like an exponentially growing snowball. Therefore, compound interest can financially reward lenders generously over time. The longer the interest compounds for any investment, the greater the growth.
Compound Interest Formulas
The calculation of compound interest can involve complicated formulas. Our calculator provides a simple solution to address that difficulty. However, those who want a deeper understanding of how the calculations work can refer to the formulas below:
Basic Compound Interest Formula
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
Continuous Compound Interest Formula
Where e is Euler's number (approximately 2.71828). Continuous compounding represents the mathematical limit that compound interest can reach within a specified period.
Useful Tips & Knowledge
Different Compounding Frequencies
Interest can compound on any given frequency schedule but will typically compound annually or monthly. Compounding frequencies impact the interest owed on a loan. For example, a loan with a 10% interest rate compounding semi-annually has an interest rate of 10% / 2, or 5% every half a year.
The interest rates of savings accounts and Certificate of Deposits (CD) tend to compound annually. Mortgage loans, home equity loans, and credit card accounts usually compound monthly. Also, an interest rate compounded more frequently tends to appear lower. For this reason, lenders often like to present interest rates compounded monthly instead of annually.
Our compound interest calculator above accommodates the conversion between daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous compounding frequencies.
History of Compound Interest
Ancient texts provide evidence that two of the earliest civilizations in human history, the Babylonians and Sumerians, first used compound interest about 4400 years ago. However, their application of compound interest differed significantly from the methods used widely today.
Historically, rulers regarded simple interest as legal in most cases. However, certain societies did not grant the same legality to compound interest, which they labeled usury. For example, Roman law condemned compound interest, and both Christian and Islamic texts described it as a sin.
Nevertheless, lenders have used compound interest since medieval times, and it gained wider use with the creation of compound interest tables in the 1600s. Another factor that popularized compound interest was Euler's Constant, or "e." Mathematicians define e as the mathematical limit that compound interest can reach.
Jacob Bernoulli discovered e while studying compound interest in 1683. Leonhard Euler later discovered that the constant equaled approximately 2.71828 and named it e. For this reason, the constant bears Euler's name.