# Continuous Compound Interest Formula

## Continuous Compound Interest Formula

The purpose of this article is to discuss the Continuous Compound Interest Formula and its derivation. If compound interest is calculated and reinvested into an account’s balance on a continuous basis, it can reach an infinite number of periods. In practice, this may not be possible. Finance, however, places a high value on continuously compounded interest. This is certainly an extreme case of compounding. In most cases, interest compounds on a monthly, quarterly, or semi-annual basis. As a result of continuously compounded interest, a particular account balance earns interest continuously and also refeeds that interest back into the balance so that it earns interest as well.

## What is Continuous Compound Interest?

The term “continuous compound interest” refers to general compound interest compounding infinitely many times each year. One receives payments with each possible increment of time due to compound interest. In continuous compounding, interest is calculated by assuming constant compounding over an infinite number of periods instead of calculating interest on a finite number of periods. There can be a finite number of periods, such as a year or a month. With very large investment amounts, the difference in the total interest earned through continuous compounding is certainly not significant when compared to traditional compounding. The continuous compound return occurs when the interest earned on an investment is calculated and reinvested for an infinite number of periods. A percentage of the principal amount is used to calculate interest. In addition, interest accumulates over time and is reinvested into the cash balance over time.

### Continuous Compound Interest Formula

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### Continuous Compound Interest Formula Derivation

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### Solved Examples

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