Compound Interest Formula

[Deleted member 4993]

I'm trying to keep this simple:
First of all P + Pr has a common factor of P, so it can be expressed as P(1 + r).

I want to know how the "P" gets in front of (1 +r) to become P(1 + r). If I divide P + Pr by P, I get (1 + r), so how does the P get in front of (1 + r) as in P(1 + r)?

I think the confusion is arising from the fact that - we are not explicitly using the "multiplication" sign (which in computers is expressed by '*' symbol).

It should be explicitly written as:

P + Pr \(\displaystyle \ \ \to \ \ \)(writing multiplication explicitly\(\displaystyle \to \ \ \)) = P + P*r = P*1 + P*r = P * (1 + r) \(\displaystyle \ \ \to \ \ \)(removing '*' making multiplication implicit)\(\displaystyle \to \ \ \)= P(1+r)

 

[Explain this!]

P=P*1

P + Pr = P*1 + Pr = P(1+r). The P was factored out.

I found this online calculator (QuickMath.com) and entered P + Pr to simplify. The result is P(P/P + Pr/P). This simplifies to P(1+ i).
I do not know why the first "P" appears before (P/P + Pr/P).

How would anyone know that a "P" goes in front of (P/P + Pr/P)?

 

[Deleted member 4993]

Yes, I ask a lot of questions!

And I answer those by posing more questions - without looking for a spoon.....

 

[JeffM]

I found this online calculator (QuickMath.com) and entered P + Pr to simplify. The result is P(P/P + Pr/P). This simplifies to P(1+ i).
I do not know why the first "P" appears before (P/P + Pr/P).

How would anyone know that a "P" goes in front of (P/P + Pr/P)?

Quickmath seems to be a remarkably clumsy tool.

At the level of math that you are discussing, an expression represents a number you do not know YET.

When you "simplify" an expression, you are trying to find a different expression that represents the same number, but is "simpler" in some respect.

In this case all you need to do is use the distributive law I told you about before.

However, three other basic laws of arithmetic are

[MATH]a \ ne 0 \implies a * 1 \equiv a,\ \dfrac{a}{a} = 1, \text { and } a * \dfrac{1}{a} = 1.[/MATH]
The first applies to any number. The other two apply to any number but zero.

[MATH]P+ Pr = 1 * P + 1 * Pr) = \dfrac{P}{P} * P + \dfrac{P}{P} * Pr = \\ P * \dfrac{1}{P} * P + P * \dfrac{1}{P} * Pr = \\ P * \left ( \dfrac{1}{P} * P + \dfrac{1}{P}\dfrac{1}{P} * Pr \right ) = \\ P * \left ( \dfrac{P}{P} + \dfrac{P}{P} * r \right ) = \\ P * (1 + 1 * r) = P * (1 + r) = P(1 + r). [/MATH]
It is just a ridiculously obscure way to say

[MATH]P + Pr = P(1 + r).[/MATH]
[MATH]24 = 3 + 21 = 3(1 + 7) = 3 * 8.[/MATH]

 

[Steven G]

I found this online calculator (QuickMath.com) and entered P + Pr to simplify. The result is P(P/P + Pr/P). This simplifies to P(1+ i).
I do not know why the first "P" appears before (P/P + Pr/P).

How would anyone know that a "P" goes in front of (P + Pr)?

P*1 + Pr = P(1+r). I underlined the terms. They are separated by the addition symbol. You asked How would anyone know that a "P" goes in front of (P + Pr)? The answer is by visual inspection. Both terms have a P in them so that goes in front. After the P you put what is left over inside parenthesis.