Different versions of the Compound Interest Formula.
The general formula is: T = P(1 + I/n)Yn
where: T = Total amount of money
P = Principle amount of money
I = Interest as a decimal.
n = How often interest is calculated in a year.
Y= Number of years.
This formula can be used to calculate the total amount of money a single investment will be worth if values for P, I, n and Y are given.
What if we wanted to find P instead? There are several practice problems that ask you to find P. The best way to tackle these problems would be to solve T = P(1 + I/n)Yn for P and use that formula for those problems.
Here is how we get that formula.
We want P alone and what we have is P times another number so divide.
We can use this formula to find P if we are given T, I, n and Y.
We can also use this formula to find I. This is a little tougher and it involves a technique that hasn’t been fully explored in this course.
We want to get I alone but it is inside the group that has the exponent Yn. We can move the P by dividing.
We now have
We need to do something about the exponent. Let’s use a simpler equation to demonstrate the method to be used.
Find the exponent that makes the following equation a true statement. (34)x = 3
First, let’s review one of the rules of exponents that was introduced in Module 3.
Multiply the exponents: (34)5 = 34·5 = 320
Therefore, (34)x = 34x and 34x = 3 = 31
To find x we can solve the equation: 4x = 1
Thus x = ¼ and (34)1/4 = 3.
How do we use this? Well, we have the equation . To get the variable I out of the group we need the exponent to be 1. This can be done be the exponent 1/Yn to both sides of the equation.
which simplifies to. We’re now two steps from the formula we’re looking for.
We can use this formula to find I if we are given T, P, n and Y.
The formula to find Y is developed in Unit 4 of this Module 8.
Here are all the formulas that are related to calculating Compound Interest.
is used when P, I, n and Y are given.
is used when T, P, Y and n are given.
is used when T, I, n and Y are given.
is used when T, P, I and n are given.
These formulas are used to solve the practice problems for Units 2 and 4.