is there an easier way to do this calculation?

[adambeazley]

I have a calculation that is working, but it is so long and I am just wondering if there is a better way. Basically, the calculation take a yearly bill and a given inflation rate and calculates how much is spent over 5, 15 and 25 year periods.

 

Here is my code:

$inflrate = 1.05; //5% inflation

//calculate yearly bill
$yearlybill = $avg_bill * 12; //total estimated yearly cost

$cost5 = $yearlybill + $yearlybill * $inflrate + $yearlybill * pow($inflrate,2) + $yearlybill * pow($inflrate,3) + $yearlybill * pow($inflrate,4);

$cost15 = $yearlybill + $yearlybill * $inflrate + $yearlybill * pow($inflrate,2) + $yearlybill * pow($inflrate,3) + $yearlybill * pow($inflrate,4) + $yearlybill * pow($inflrate,5) + $yearlybill * pow($inflrate,6) + $yearlybill * pow($inflrate,7) + $yearlybill * pow($inflrate, + $yearlybill * pow($inflrate,9) + $yearlybill * pow($inflrate,10) + $yearlybill * pow($inflrate,11) + $yearlybill * pow($inflrate,12) + $yearlybill * pow($inflrate,13) + $yearlybill * pow($inflrate,14);

$cost25 = $yearlybill + $yearlybill * $inflrate + $yearlybill * pow($inflrate,2) + $yearlybill * pow($inflrate,3) + $yearlybill * pow($inflrate,4) + $yearlybill * pow($inflrate,5) + $yearlybill * pow($inflrate,6) + $yearlybill * pow($inflrate,7) + $yearlybill * pow($inflrate, + $yearlybill * pow($inflrate,9) + $yearlybill * pow($inflrate,10) + $yearlybill * pow($inflrate,11) + $yearlybill * pow($inflrate,12) + $yearlybill * pow($inflrate,13) + $yearlybill * pow($inflrate,14) + $yearlybill * pow($inflrate,15) + $yearlybill * pow($inflrate,16) + $yearlybill * pow($inflrate,17) + $yearlybill * pow($inflrate,18) + $yearlybill * pow($inflrate,19) + $yearlybill * pow($inflrate,20) + $yearlybill * pow($inflrate,21) + $yearlybill * pow($inflrate,22) + $yearlybill * pow($inflrate,23) + $yearlybill * pow($inflrate,24);

 

So basically $cost5 would return the total amount the person would pay in 5 years with the same inflation rate (which would compound every year).

 

So, my question is, is there some function that i dont know about that would cut this code down to a single line? I want to get the total cost for 5, 10, 15, 20 and 25 years, but i dont want 10 pages of repeating code like this.

 

Also, if there is any way I could have a function where i could simply input the number of years and get a result, that would be ideal.

 

Thanks

 

 

[DarkWater]

Well, if you were doing this on paper, it would be:

[tex]P = 5000\left(1 + .05\right)^t[/tex]

 

Where 5000 is the yearly bill and t is the amount of years.  Correct?

[Daniel0]

You would want to look up what exponential growth is. Generally speaking, when something grows with a specific percentage then it's growing exponentially, because it will grow "more" each time. That's opposed to grow with a constant factor, which would then be linear.

[DarkWater]

Yeah.  The only reason that I did 1 + .05 instead of 1.05 is because I was originally compounding it monthly for some reason.  Didn't read the question that carefully. xD

[Daniel0]

Wasn't for you. Yours was entirely correct

[sasa]

<?php
$inflrate = 1.05; //5% inflation

//calculate yearly bill
$yearlybill = $avg_bill * 12; //total estimated yearly cost

$cost5 = $inflrate != 1 ? $yearlybill * (pow($inflrate,5) - 1) / ($inflrate - 1) : $yearlybill * 5;

$cost15 = $inflrate != 1 ? $yearlybill * (pow($inflrate,15) - 1) / ($inflrate - 1) : $yearlybill * 15;

$cost25 = $inflrate != 1 ? $yearlybill * (pow($inflrate,25) - 1) / ($inflrate - 1) : $yearlybill * 25;
?>

[adambeazley]

Thanks again Sasa! that worked great, give me the same answer but so much less code.

 

@DarkWater your equation is partially right P = 5000(1 + .05)^t will give you the total that was spent that year (t). As I mentioned in the question this is a compounding interest equation, so if you want to get how much was spent over 5 years this is the equation (mathematically):

P = 5000 + 5000(1 + .05) + 5000(1 + .05)^2 + 5000(1 + .05)^3 + 5000(1 + .05)^4

 

1st year = 5000 (not counting inflation)

2nd year = 5000 * 1.05

3rd year = 5000(1.05)^2

4th year = 5000(1.05)^3

5th year = 5000(1.05)^4

 

Anyway, Im sure you already know this stuff, but just in case someone is searching forums in need of an answer this might help.

 

Peace guys and thanks allot for the help!!!

 

 

[corbin]

"this is a compounding interest equation"

 

Technically his was a compounding interest equation.

 

 

The interest compounds in his.  In yours, the interest compounds, and each number is added back to the sum.

[DarkWater]

I know you already have an answer, but I think I just worked out a slightly shorter way to get it.

 

Let's say that A is $yearlybill, r is $inflrate, n is the number of years and P is the cost

 

[tex]P = \displaystyle\sum_{i=0}^n A\left(r\right)^i[/tex]

 

We can move the A out:

[tex]P = A\displaystyle\sum_{i=0}^n r^i[/tex]

 

And then we can simplify the sum to:

[tex]P = A\left(\frac{1-r^{n+1}}{1-r}\right)[/tex]

 

So basically:

[tex]P = 5000\left(\frac{1-1.05^6}{1-1.05}\right)[/tex]

 

I got 34009.5640625. Is that the number you get with your code? If it is, then this expression is very easy to put into PHP.