#### Explain this!

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- Thread starter Explain this!
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Where did you see that "happening"? I think you are misquoting!

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I've seen this or something similar to it in finance books. Think of it in another way. Where does P(1 + i)^n - 1 come from? Isn't this the compound interest formula?Where did you see that "happening"? I think you are misquoting!

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However, you have NOT seenI've seen this or something similar to it in finance books. Think of it in another way. Where doesP(1 + i)^n - 1come from? Isn't this the compound interest formula?

Most probably you have seen

Compound interest after

Those

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Thanks for the reply! I'll search for an answer, but I thought that is what you "experts" are for -- to answer questions. Is there a simple reason why the brackets are important?However, you have NOT seenthat

Most probably you have seen

Compound interest afternperiod = P[(1+i)^n-1]

Those[]are super-important. Now that you know the correct expression - google around a bit, you can find the derivation.

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"...I thought that is what you "experts" are for -- to answer questions"Thanks for the reply! I'll search for an answer, but I thought that is what you "experts" are for -- to answer questions. Is there a simple reason why the brackets are important?

Nope ... we are volunteers - we "choose" our actions - we GUIDE.

And we refuse to spoon-feed.....

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Yes . without parentheses - you'll get a different numerical answer.Is there a simple reason why the brackets are important?

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The very simple reason that you will get it wrong if you do not follow the order of operations.Is there a simple reason why the brackets are important?

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I'm certainly glad that I do not have you as an instructor, if that is your occupation!"...I thought that is what you "experts" are for -- to answer questions"

Nope ... we are volunteers - we "choose" our actions - we GUIDE.

And we refuse to spoon-feed.....

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The "gladness" is mutual.I'm certainly glad that I do not have you as an instructor, if that is your occupation!

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Yes, I ask a lot of questions!The "gladness" is mutual.

It doesn't. You are mixing up different formulas.

\(\displaystyle (P + Pi) - P = Pi\).

That is the formula for calculating the interest paid on amount P for one period

30000 dollars for one month at 1/4 % per month. What's i?

\(\displaystyle 100 * i = \dfrac{1}{4} = 0.25 \implies i = \dfrac{0.25}{100} = 0.0025.\)

So the interest paid is \(\displaystyle 30000 * 0.0025 = 75.\)

The other formula, which you got wrong, is

\(\displaystyle P\{(1 + i)^n - 1\}.\)

That is the formula for interest paid after n periods when interest at a rate of 100 * i percent per period is

30,000 for 3 months at an interest rate of 1/4 % per month compounded monthly will involve payment of interest after 3 months of

\(\displaystyle 30000\{(1 + 0.0025)^3 - 1\} = 225.76 > 3 * 75.\)

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It doesn't. You are mixing up different formulas.

\(\displaystyle (P + Pi) - P = Pi\).

That is the formula for calculating the interest paid on amount P for one periodwithout compoundingat an interest rate of 100 * i percent per period.

30000 dollars for one month at 1/4 % per month. What's i?

\(\displaystyle 100 * i = \dfrac{1}{4} = 0.25 \implies i = \dfrac{0.25}{100} = 0.0025.\)

So the interest paid is \(\displaystyle 30000 * 0.0025 = 75.\)

The other formula, which you got wrong, is

\(\displaystyle P\{(1 + i)^n - 1\}.\)

That is the formula for interest paid after n periods when interest at a rate of 100 * i percent per period iscompoundedrather than paid before maturity.

30,000 for 3 months at an interest rate of 1/4 % per month compounded monthly will involve payment of interest after 3 months of

\(\displaystyle 30000\{(1 + 0.0025)^3 - 1\} = 225.76 > 3 * 75.\)

My question is what is the original formula that becomes P{(1 + i)^n - 1} and how does it become P{(1 + i)^n - 1}?

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I have no idea what your reply indicates.I can give you an intuitive answer or a proof by weak mathematical induction.

Does P + Pr = P(1 + r)? If yes, then can you show me the steps?

I can show you an answer for n = 2, or n = 3, but that is not a general answer. The way to give a general answer is through weak mathematical induction.

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I'm trying to keep this simple:

I can show you an answer for n = 2, or n = 3, but that is not a general answer. The way to give a general answer is through weak mathematical induction.

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)?

3 * (6 + 8) = 3 * 14 = 42.

Now you can try experimenting with other numbers until you have convinced yourself of the validity of this basic law of arithmetic:

\(\displaystyle a(b + c) \equiv ab + ac.\)

It's called the distributive law of multiplication over multiplication.

There is a proof using induction and the Peano Postulates, but I have long since forgotten it.