Convert an interest rate from one compounding frequency to another.
Interest is the cost of borrowing money. Simple interest is calculated only on the principal, while compound interest is calculated on both the principal and the accumulated interest.
Compound interest is like a snowball rolling downhill—it grows exponentially over time because you earn interest on your interest.
Example: $100 at 10% compounded annually for 2 years:
Total compound interest = $21 vs. $20 with simple interest.
The more frequently interest compounds, the higher the effective annual rate (APY). A 10% rate compounded semi-annually is equivalent to 10.25% compounded annually.
Mortgages and credit cards often compound monthly. Savings accounts may compound daily. Continuous compounding represents the mathematical limit of compounding frequency.
Basic formula (periodic compounding):
Continuous compounding formula:
A quick way to estimate how long it takes for an investment to double: divide 72 by the annual interest rate. For example, at 8% interest, it takes about 72/8 = 9 years to double.
The Babylonians and Sumerians used compound interest over 4,400 years ago. However, many ancient societies, including the Romans, considered it usury. The concept became more widespread with the creation of compound interest tables in the 1600s.
Jacob Bernoulli discovered the mathematical constant e in 1683 while studying continuous compound interest. Leonhard Euler later named it e and calculated its value to be approximately 2.71828.