Types of Interest: Simple and Compound Interest
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In this article, mathematical formulas are used to describe types of interest based on how they accumulate or accrue. Let's find out the difference between simple and compound interest.
Simple Interest
Simple interest is, well, the simplest and most basic kind of interest out there. You can calculate simple interest by multiplying Principal by Rate by Time, given by the following formula:
I = P x r x t
Here, principal (P) is the amount to begin with, whether it's invested, lent, or borrowed. This amount increases by the given interest rate (r) over a period of time (t). To calculate not just the accrual but the resulting amount to which interest is applied, you can use the amount function:
A(t) = A0 x (1 + t x r)
In the given formula, A0 is the principal, while r and t are the interest rate and period of time, respectively.
Because simple interest is a linear function, it is quite easy to see how a loan or an investment will turn out in the future.
Compound Interest
Described as "the most powerful force in the universe" according to Albert Einstein, compound interest is a bit more tricky to calculate. Interest is periodically added to the current amount, and the amount you get (or owe) is computed from the following formula:
A(t) = A0 x (1 + r/n)n x t
The principal (A0) increases by an amount that is dependent on both the given interest rate (r) and the number of compounding periods (n) within a given time period. This time (t) is usually expressed in years. So if a starting amount, $500 were to be compounded at a monthly rate of 5% for five years, n would be equal to 12 and t would be equal to 5. The equation would be: A(t) = 500 x (1 + 0.05/12)5 x 12 and amounts to $641.68.
Instead of a linear rate being applied, we see an exponential growth: notice that each time the amount A(t) is compounded by an interest rate dependent on that current amount A(t). In investing, that sounds like a good way to make your money grow. In borrowing, however, that doesn't sound that great.
What is APY?
Because we know how tricky it is to figure out the additional amount added to the principal in a compounded interest scheme, calculating the annual percentage yield or APY proves to be a helpful method in calculating the yield, or the extra amount, and not the total resulting amount. You can get your APY through the following equation:
APY = (1 + r/n)n – 1
Again, r stands for the interest rate and n is the frequency of compounding that occurs in a year. Calculating APY gives you a better idea of how much you earn or how much more you owe in relation to the principal.
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