Ib Credits (ore) And Interest

[Hooman]

Ok, so I was a little bored and decided to think about when to buy more interest at the IB store so as to maximize your amount of ore.

Taking money out of your bank will of course decrease your base of money from which to gain interest from. However, you will receive more interest on what is left. So at what point is it best to spend the money on more interest? It's certainly not optimal to buy more interest as soon as you can. If you up your interest as soon as you get 500 ore, you're now making 5% of nothing, which is nothing. If you hadn't upgraded, you'd be getting 3% of 500 ore which is 15 ore. Also, 5% of say, 999500 ore will give you way more 3% of 1000000 ore.

Well, if we think about it, the idea of buying interest is to increase the amount of money you get from interest. So if buying that interest leads to receiving less interest than you'd be getting without buying the upgrade, what was the point? Similarly, what's the point in delaying buying interest, if buying it now will increase the interest you're currently receiving.


The idea is to find when the interest before the purchase is equal to the interest after the purchase. Then you know how much ore to save up before buying more interest.

Suppose x is the current amount of ore you have, p is the price of the interest upgrade, r1 is the rate of interest before the upgrade, and r2 is the rate of interest after the upgrade. Then:
x * r1 = (x-p) * r2
x * r1 = x * r2 - p * r2
x * (r1 - r2) = - p * r2
x = (- p * r2) / (r1 - r2)
x = (p * r2) / (r2 - r1)

So given any p, r1, and r2, we may calculate x, the optimum amount of ore you should have when buying more interest.


If we use knowledge that interest always increases by 2% then r2 - r1 will always be 0.02. Also, we might want to fix p at 500 (the current price of interest). If you want to account for the widthdrawl fee, increase p a little (about 508). Then the formula above can be simplified a little.
x = (500 * r2) / (0.02)
x = 25000 * r2

So, the optimum point at which to upgrade from 3% to 5% interest is: x = 25000 * 0.05 = 1250 ore. Also, since this function is linear, an all increase in interest are by 2% (that is, r2 increases by 0.02 each time), and 25000 * 0.02 = 500, then for each 2% increase in interest, you should do it at a point 500 ore beyond the last time interest was upgraded.

r2 = 5%, x = 1250
r2 = 7%, x = 1750
r2 = 9%, x = 2250
...



Any thoughts on this?  B)

[Betaray]

wow, and I thought I was bored lol

good work

[Hooman]

Thanks.

Although, I'm wondering if maybe I should have kept this to myself.  :unsure: Well, at least I can use the concept of this post to estimate how much interest other people have bought based on how much ore they stock in their bank. At least assuming they've read this and follow the advice.

I'm not too sure how to work other items into this idea though. Like the auto collect interest. I guess that depends on how often you miss collecting.
 

[Betaray]

well you dont have to worry about me, I'm too impatiant to get 1250 ore the old fashoned way

of corse, i could in about a day if I went back to my old ways, but I dont think lev or hacker would like that lol

[Eddy-B]

looks like u got some time on ur hand - and you dont know what to to with it, hooman

[BlackBox]

When you say "buy interest" - are you talking about the upgrade interest? or just hitting the collect button?

I don't really see why you'd want to see that you had a specific amount of money when you upgraded - since upgrades are permanent.

Eg. if you're at 3% interest and you buy a 2% upgrade, you're now making 5% interest for the rest of your account's life.

And I can't see how it would be possible to receive less interest than you had before you upgraded - the rate is higher!

(Well, sure in the short time, i.e. if you take money out of the bank to pay for the upgrade, but in the long run you'd get more as you deposited more money).

I just don't understand why a calculation like this would be needed - the increase is permanent.

[CK9]

hacker, he is talking about the short run there.  The problem with hooman's equation is that it is linear.  Intrest-ore relation is on a curve.  If you don't believe me, graph your earnings on an x-y plane.  set y as ammount of ore and x as days.  For it to work, you will need to collect your interest every day you graph it.  I'd suggest at least a week so the curve is more apparent.

[Betaray]

somthing tells me that the function e the 2.7... number is involved in this

[Hooman]

LOL.

Seems my idea is a little less understood than I expected. Hacker, yes, this is the short term. However, the short term gains will lead to long term gains if the only thing you're doing is buying interest upgrades every so often.

The idea was, if all you do is post, get ore, and collect interest on what's in the bank, and assuming everything you have is stored in the bank earning interest, then that is how much money you should keep sitting around before you upgrade your interest.

i.e. If you have only 500 when you upgrade, you're now making 0 ore in interest. If you kept that 500 in the bank and didn't buy interest, then you'd actually be making interest on the ore in your bank. So buy buying more interest (percentage wise), you've decreased your interest (in terms of ore gained the next time you collect).


Yes, it is a linear model, but what my model represents isn't compounded interest. It's representing the ore you get the next time you collect based on current ore and interest. It's to answer a simple question. Would I get more ore the next time I collect if I bought interest (upgrade) now, or if I waited to buy more interest later. It's a simple descision rule for when to buy interest. Should I buy interest (upgrade) now? Yes or No.

If you think about it, this decision really has no long term considerations required. You're maximizing your interest at any given moment, which will lead to maximizing interest overall in the long term.
 

[CK9]

true, the intrest does build up better if you are maximizing at the point of increase, but, because it is still a linear thing, does it really make a big impact for the lower ammounts of ore?

[Hooman]

This makes no difference on your current amount of ore. If you have none, you still get none from interest. This really only applies to people who have money in the bank. Certainly if you can't afford to buy an interest upgrade, then this doesn't apply to you. This is for people who can buy the upgrade, but might not be sure when it's most benficial to buy it.

Edit: Oh, and yeah, this can have quite an impact on your rate of ore growth. But that also depends on your posting habits too.
 

[Stormy]

I just did that, It got me the same interest I was getting with 1280 ore

w00t

stormy :op2:

[Hooman]

Yes..., you're becomming too much of a thread Stormy!  :ph34r:

Lol, jk. Have fun with it.  B)  

[BlackBox]

somthing tells me that the function e the 2.7... number is involved in this

Not that I can see. It's not compounded continuously.

e would only make sense in the compound interest formula (for those of you who need a refresher):

[doHTML]A = Pe^rt[/doHTML]

I guess you could say it's compounded daily, if you were to collect interest every day:

[doHTML]A = P(1 + r/365)^365t[/doHTML]

(For both formulas, A is your new principal (old + interest), P = old principal, e = obviously Euler's constant, r = rate percentage (expressed in decimal form, i.e. 5% = .05), t = time in years)

And it makes sense now. for short term gains. I was thinking you were trying to calculate it for long term since it wouldn't make much sense to go thru the whole process of calculating when you KNOW your interest is gonna be higher in the long term.

Oh btw, I might add:

I think when you buy an upgrade to interest, you can't collect interest for that day. Same if you deposit money in the bank, the timer gets reset. That would affect your interest collection whenever you did those things. (I'm not certain about the buying upgrades. Depositing does reset the timer though)

[CK9]

AG!  I thought I had escaped the interest formulas!

[Hooman]

Lol, CK9.

And Hacker, that's why you collect interest BEFORE you deposit or buy upgrades.    

[CK9]

but don't try to buy things from beta or hooman instead of the store, you'll get egss instead either way, lmao

[Hooman]

egss? I can only assume from the reference to Beta that you meant eggs. But, why would I give anyone eggs?  :blink:  

[CK9]

hooman, think about it.  Look at your avatar while thinking