# Continuous Compound Interest

** Enter percentages as whole numbers, i.e. 5% should be input as 5. The calculator converts percentages to decimal form.

## What is Continuous Compounding Interest?

Continuous compound intest assumes that interest is continuously applied to the principal, so you are continuously earning interest on your interest (and principal). Principal is the initial amount invested. It assumes a theoretical infinite number of periods where the interest is continuously applied to the balance of an account (principal plus previously earned interest). In the "real-world" this formula is primarily used for options pricing. Outside of this, it is taught as a concept that illustrates the power of compounding interest over time.## Continuous Compound Interest Formula

To solve a problem seeking continuous compound interest, the formula is:

A = Pe

^{rt}

where,

A = Amount of future value

P = Initial amount invested

e = Stands for Napier's number and is approximately 2.7183

r = Interest rate

t = Length of time investment will accrue

## Sample Continuous Compound Interest Problem

Nolan worked hard this summer and was able to earn $3,500 from mowing lawns. He would like to invest it so when he gets older he can use the money toward a down-payment for buying a house. He talked with his parents and the discussed the idea of investing the money in an S&P fund. Based on historical averages, the return rate is about 10%, keeping in mind this is an annual rate of return. After talking with his parents he decided this is where he wanted to put his money, so he opened an account. How much money will Nolan have in 8 years?A = $3,500 * 2.7183

^{.1 * 8}

As a result of continuous compounding interest he will have $7,789.39 at the end 8 years.

***Disclaimer: Of course this assumes the rate of return is continuously applied... this is a theoretical example!