Explain this!
Junior Member
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- Feb 7, 2019
- Messages
- 164
How does (P + Pi) - P become P(1 + i)^n - 1? I know that factoring is involved, but I not sure what the steps are.
Where did you see that "happening"? I think you are misquoting!How does (P + Pi) - P become P(1 + i)^n - 1? I know that factoring is involved, but I not sure what the steps are.
Where did you see that "happening"? I think you are misquoting!
However, you have NOT seen thatI'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?
However, you have NOT seen that
Most probably you have seen
Compound interest after n period = 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.
"...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?
Yes . without parentheses - you'll get a different numerical answer.Is there a simple reason why the brackets are important?
Is there a simple reason why the brackets are important?
"...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.....
The "gladness" is mutual.I'm certainly glad that I do not have you as an instructor, if that is your occupation!
The "gladness" is mutual.
It doesn't. You are mixing up different formulas.How does (P + Pi) - P become P(1 + i)^n - 1? I know that factoring is involved, but I not sure what the steps are.
It doesn't. You are mixing up different formulas.
[MATH](P + Pi) - P = Pi[/MATH].
That is the formula for calculating the interest paid on amount P for one period without compounding at an interest rate of 100 * i percent per period.
30000 dollars for one month at 1/4 % per month. What's i?
[MATH]100 * i = \dfrac{1}{4} = 0.25 \implies i = \dfrac{0.25}{100} = 0.0025.[/MATH]
So the interest paid is [MATH]30000 * 0.0025 = 75.[/MATH]
The other formula, which you got wrong, is
[MATH]P\{(1 + i)^n - 1\}.[/MATH]
That is the formula for interest paid after n periods when interest at a rate of 100 * i percent per period is compounded rather 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
[MATH]30000\{(1 + 0.0025)^3 - 1\} = 225.76 > 3 * 75.[/MATH]
I can give you an intuitive answer or a proof by weak mathematical induction.
I can show you steps if you understand weak mathematical induction. You do realize that n can be any of an infinite number of values. I am not going to show you detailed steps for when n = 365.
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.