Compound Interest

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Continuously Compounded Interest

Mathematics: MATH650 section 02
Wendy Forbes
April 27, 2010

We often hear people say that we should let our money work for us. Using money or capital for income or profit is called an investment.

An accountant manages a company’s money. Then, managers or company investors review their reports to find out the financial status. The demand for accountants increases as more private companies are established. In addition, there are always new and changing laws that increase the need for a person with these skills.

Continuously Compounded interest is what banks normally use to calculate the interest on investments. This method is the equal of continually recalculating the interest based on the current principal amount.

There are different types of Compound Interest. Interest is the amount of money earned in a saving account. * Simple Interest: Interest calculated once on the principal. * Compound Interest: Interest calculated for a given segment of time of the investment. For example, compounded monthly, means the interest is calculated each month and combined with the principal. So, for the next month, interest is earned on the interest.

Continuously Compound Interest Formula

P: ending principal
P0: initial principal
e: constant e
k: interest
t: time as measured in years

Example problem:
Let’s say your accountant invests $5,000.00 in a saving account at a bank for you that earns 5% interest compounded continuously. How would we know what is earned after 10 years?

We start with our formula.

* We determine the values for each of the variables in the formula: * P0 = $5000.00Initial principal
* k = 5% but use the decimal equivalent 0.05
* t = 10Number of years
* e is a special number used to get the natural exponential growth. It is used throughout math and is approximately 2.7183.
Also, it is usually...
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