Question

What do you mean by Geometric Progression in math on investment? what is the logic behind the formula if any?

Answer 1

I've had my share of geometric progressions, but you may have to be a little more specific about the details you want ^_^

Answer 2

I don't know how to use the formula of geometric progression in terms of Annuities. :)

Answer 3

Sounds like college stuff D:

Answer 4

yeah. our group report is about Simple case for Annuity and I'm assigned to report about Geometric progression.

Answer 5

How old are you? D:
(curious)

Answer 6

Because this already reeks of work stuff, actually. Annuity (yech)

But anyway....

Answer 7

Do you know the definition of a simple annuity?
A series of level payments made at the end (or maybe beginning) of each period... that annuity, yes?

Answer 8

yes. youre right :D

Answer 9

No, I'm TJ.
Who in their right mind would name someone "right" ? :/


LOL

I need to know that you know your basics first, though.

If we have a rate of interest i, do you know the present value of an amount 1 given at time n?

Answer 10

Oi, <snaps fingers>
stay with me here... or are you totally lost? :D

Answer 11

Sorry. I just cant get over your joke a monment ago. hahaha

Answer 12

That's a poor excuse for slacking off >:(
But seriously, you know the concept of 'present value' ?

Answer 13

sorry :( but not quite

Answer 14

Tengo una pregunta... hablas español?

Answer 15

what?

Answer 16

Never mind, I thought you spoke Spanish what with your name sounding all spanish-y

Anyway, if we have an interest rate, say i, per year, then I give you an amount 1 right now.

Then next year, the amount will have increased to 1+i, correct?

Answer 17

yes

Answer 18

Yes, you speak Spanish? :3
LOL kidding.

So what about after n-years, to what amount will the money have grown?

Answer 19

Haha. i dont know.

Answer 20

Perhaps a more concrete case would help you :)
Say, for a moment, you invest just an amount 100.
With an interest rate of 5% per year.
Next year, it'd increase to 105, yes?

Answer 21

Also, this is in no way related to your question, but where ARE you from, if you don't mind me asking? :/

Answer 22

yup :)

Answer 23

What about the second year?

Answer 24

And my unrelated question still stands :3

Answer 25

you seem very curious. am I weird?

Answer 26

Of course you are, and that's fine, I bet I'm weirder anyway. I'm just naturally curious

Answer 27

why is that?

Answer 28

I'm just betting... it doesn't have to be true...

And I still have two questions that you haven't answered... (one of them linked with your predicament... chop-chop now :3 )

Answer 29

what do you mean about the second year?

Answer 30

second year.
First year, 100 becomes 105.
Second year, 105 becomes... what?

Answer 31

Might I register my astonishment that you're working with annuities without a working knowledge of theory of interest D:

Answer 32

You should totally kill your instructor >:D

Answer 33

what?

Answer 34

205 i guess

Answer 35

haha no way.

The world will crumble if that were true :P

Answer 36

Imagine, investing your money and in two years, you get more than double?!

Try and stay reasonable :P

Answer 37

Hahahaha. I feel so dumb while talking to you :( :)

Answer 38

well. that can happen :P

Answer 39

Not my intention miss... whatever (apologies if you turn out to be a boy... I'm just making guesses here)

Anyway, shall we start from the beginning again? :D

Answer 40

yea :)

Answer 41

Let me make it easier for you.
First, we don't work with percentages... turn them into decimals IMMEDIATELY.
5% is just 0.05, comprendes?

Answer 42

and yea, im a girl. i think so. hahaha

Answer 43

yes

Answer 44

Okay, now what we did to turn 100 to 105 was simply multiply 1+i to the original amount.
i here being equal to 0.05.

So... 100 times 1.05 is...?

I'll save you time, it's just 105, as it should be.

Now, at the second year, you simply do it again, multiply 105 by 1.05, and you get the amount at the end of the second year, which is 110.25


Entiendes?

Answer 45

While we're here, might as well learn some spanish, since, well, no reason :P

Comprender and Entender both mean 'to understand'

LOL

But did you understand that previous post^ ?

Answer 46

i get it now. Gracias (am i right?)

Answer 47

Si, eres correcta. ^_^
Bueno...

Now, let's be a little bit more general, ready?

Answer 48

i went to spanish class one time

Answer 49

okay.

Answer 50

If you have to go to Spanish class, then obviously, you aren't a native speaker...
So where ARE you from?
You're leaving me hanging here :P

...Anyway
the more general case, is not the first year, not the second year, the nth year.
Turns out, after n years, 100 accumulates to a value
\[\Large 100(1.05)^{n}\]

ok?

Answer 51

okay :)

Answer 52

you have guess Im a girl, i think you can guess that too.

Answer 53

Here's the thing, when guessing genders, there are only two of them, so, there's a 1/2 chance of getting it right. With countries involved, there are 193 of them. Of course, I can eliminate 20 Spanish-speaking countries, that still leaves a staggering 173 countries, so trying to guess where you're from is basically blind-guessing, so why don't you just humour me? :3



Now, let's be more general.
If we start with an amount p, and we have an interest rate r, then after n years, the amount accumulates to...
\[\Large p(1+r)^n\]

Answer 54

okay okay

Answer 55

hmm?
Are you sure?
Let it sink in for a minute or two, first.
Oh, and where in the blazes are you from? Come on, sate my curiosity :3

Answer 56

Oh, and uhh, tell me when you're absolutely ready for the next bit (which is doing it in reverse)

Answer 57

oh fudge

Answer 58

fudge? Where? :3

Answer 59

hahaha. i have another problem, do you know something about database?

Answer 60

Don't stray... we're not even close to annuities yet...
FOCUS... (ironically something I can't do... where are you from?!!)

Answer 61

I still want to test your guessing skill :3

Answer 62

but

Answer 63

I could say the same to you, you know :P
(testing YOUR guessing skill)
But that'd be a disaster on your part, wouldn't it? >:D

Answer 64

hahaha.

Answer 65

database please?

Answer 66

Honestly, I don't know what you mean by database.
I can help you (tons) with annuities, but database, not so.

And besides, you're still leaving me hanging :(

Answer 67

Guess now :) im waiting

Answer 68

hmm,. how about geometric progression :3

Answer 69

Why do you think I even took an interest in this question? :P

And should you really wait for me?
I should wait for you instead.... and not post any more while I'm still left hanging >:D

Answer 70

Well, unfortunately, my inherent and ultimately good-boy nature doesn't allow me to make good on that previous post. ^

But did you understand that bit about accumulated values though?

Answer 71

Oi, *shasha* at least say something -_-

Answer 72

Im starting to get nervous on my report :(

Answer 73

Not my problem.
Did you or did you not understand this formula:\[\Large \text{accumulated value at time n}=p(1+r)^n\]

Answer 74

Where p is the starting value, r is the rate of interest, and n, is, well, the number of years that pass.

Answer 75

ok

Answer 76

What time is it there, anyway?
I'm getting a little sleepy :/

Answer 77

10:44pm

Answer 78

Let's do it in reverse.
What if I ask you what amount you need to invest, so that you get exactly p after n years?

Answer 79

hmmm. how is that?

Answer 80

Simple algebra silly.
Let q be that amount.

Then after n years, q would accumulate to
\[\Large q (1+r)^n\] yes?

Answer 81

hm. ok

Answer 82

And after n years, we want to have exactly p. So
\[\Large q(1+r)^n = p\]
Do yourself a favour and solve for q...

Answer 83

... or not.
\[\Large q = p(1+r)^{-n}\]
Understood?

Answer 84

... not a good idea to space out on me... a fair warning... I could fall asleep anytime...

Answer 85

Im sorry

Answer 86

No you're not... but anyway, did you understand how to solve for q?

Answer 87

i understood your post thou

Answer 88

what time is it there?

Answer 89

i not done reading

Answer 90

When I ask a question, answer it asap, either with the answer, or with a statement saying you don't understand, because as much as I hate being left hanging about trivial questions such as where you're from, it's even more tiresome to be left hanging about the more serious questions...

Anyway, we call q the present value of p given at time n.

For convenience, we set this value:

\[\Large v = (1+i)^{-1}\]So that we can write\[\Large q=pv^n \]

Answer 91

Get it?

Answer 92

okay Sir

Answer 93

I'm tired lol.
The only thing keeping me from falling asleep in the middle of this tutorial is the fact that we're from the same country.

Heh...

Now... quick run-over.
IF the present value of 1 given at time 1 (in other words, next year) is v
the present value of 1 given at time 2 (in other words, two years from now) is v^2
the present value of 1 given after three years is v^3
the present value of 1 given after n years is v^n

Got it?
This is crucial.

Answer 94

very crucial. im trying to understand it

Answer 95

Sir

Answer 96

Tell me when you're ready.
And cut the "Sir" crap, it's TJ. Or Terence. Whatever floats your boat.

Answer 97

you kinda scared me earlier, that why i think it will be best to call you Sir :)

Answer 98

No, that's detrimental.
And despite my best efforts, I AM falling dangerously sleepy, so, try and understand a little faster, yeah?