Compound Interest and Several Examples of Exponential Functions
Here, we will go over some examples of Compound Interest. It is important to know that Compound Interest is just a exponential function that can be solved using simple algebra.
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| Labeled Formula of Compound Interest |
P = the principal amount, otherwise known as the original/ initial amount.
r = rate at which the money grows per year; interest rate (written in decimals)
m = number of times compounded in a year (ex. daily, biweekly, weekly, monthly, semimonthly...)
t = after how many years (amount of years)
A = the total amount after 't' years
If 'm' equals the following numbers, that is the way we are compounding in a year.
m = 1 only counted once per year, every year
m = 2 semiannually, because it is only counted 2 times a year; meaning after every 6 months (12/2=6)
m = 4 quarterly, because it is only counted every 4 times a year; meaning after every 3 months (12/4=3)
m = 12 monthly, because there are 12 months in a year, so after every month for 12 total counts in a year.
m = 52 weekly, because there are 52 weeks in a year, so after every week for 52 total counts in a year.
m = 365 daily, because there are 365 days in a year, so after every day for 365 total counts in a year.
Great, let's try an example.
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So, we have to solve for x in terms of 'm'. Let's rephrase the question into a formula. Original formula: A = P(1 + r/m)^mt Our equation: A = 200(x)^mt where x = (1 + r/m) |
We know that 'r' or rate has to be written as a decimal. So the rate HAS to be a decimal.
The answer is A.)
See? No math required on that one!
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Here's another example:
