Continuously Compound Interest
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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 or an auditor is assigned the job of managing a companys money. Then, managers or company investors examine their reports to find out how the company is doing. An accountant will have good job opportunities. 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 equivalent of continuously recalculating the interest based on the current principal.
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:
Lets suppose 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 amount is earned after 10 years?
We start with our formula.
We determine the values for each of the variables in the formula:
P0 = $5000.00
Initial principal
k = 5%
but use the decimal equivalent 0.05
t = 10
Number 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 available on your calculator.
Solution