What is continuous compounding

The following examples and the demonstration illustrate different kinds of interest and how they can be useful or harmful to investors.

Example 1: Simple Interest. The formula for the future value S of some investment with simple interest is:. Notice that r is in decimal form rather than percent form.

Example 2: Simple Interest. Therefore, at the end of the 2 years she will owe:. Example 3: Compound Interest. Rather than charging simple interest on the loan, the bank can use a more widely used form of interest calculation, compound interest. Compound interest is interest that is added to the principal of a loan such that the added interest also earns interest.

The addition of interest to the principal amount is referred to as compounding. Compound interest can also be used to your advantage. Buying guaranteed investment certificates GICs or government bonds, can make the bank pay you interest. GICs pay compound interest , which as you will see, is much better than simple interest for investments.

Example 4: Compound Interest. After the first year his investment will be worth:. The next year he will make 2. After the 12 th year however, his initial investment has grown to:.

The general formula for compound interest after n compounding periods is:. This can be further generalized for any time periods paying r interest rate per year as follows:.

Example 5: Compound vs. Simple Interest. Both will last 3 years and have an interest rate of 2. After 3 years, the simple interest GIC will pay Bob:. Here, A is the final amount.

For the continuous compound interest, the number of terms is infinite, i. We can use the button 'e' on the calculator for more accurate calculations instead of using the number 2. Continuous Compounding Formula Before going to learn the continuous compounding formula, let us recall few things about the compound interest.

What Is Continuous Compounding Formula? Continuous Compounding Formula Derivation We will derive the continuous compounding formula from the usual formula of compound interest. Become a problem-solving champ using logic, not rules.

Learn the why behind math with our certified experts. What Is e in Continuous Compounding Formula? Explore math program.

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Dividend Stocks Guide to Dividend Investing. Stocks Dividend Stocks. What Is Continuous Compounding? Key Takeaways Most interest is compounded on a semiannually, quarterly, or monthly basis. Continuously compounded interest assumes interest is compounded and added back into the balance an infinite number of times. The formula to compute continuously compounded interest takes into account four variables. Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation.

This compensation may impact how and where listings appear. Investopedia does not include all offers available in the marketplace. What the Effective Annual Interest Rate Tells Us The effective annual interest rate is the real return on an investment, accounting for the effect of compounding over a given period of time. What Is Euler's Constant? What Is Discrete Compounding?