[RESOLVED] Order of Operations and PHP

Warmaster

Ok, so I finally figured out how to make a function that returns the monthly payment on a home mortgage based on the amortization formula. I had a real rough time with the order of operations and I am curious as to shortcuts etc.

I basically had to break my formula down into small pieces based on the proper order of operations. Why can't I just put a whole formula in there and have php output the proper figures? Or is it a flaw with php?

For example I could not just divide the numerator by the denominator (separating the code with parenthesis) cause it would return 0.

Anyway, thanks for the input and helping me understand how PHP works:

<?php 
/* 
First you must define some variables to make it easier to set up:
# P = principal, the initial amount of the loan
# I = the annual interest rate (from 1 to 100 percent)
# L = length, the length (in years) of the loan, or at least the length over 
which the loan is amortized.

The following assumes a typical conventional loan where the interest is 
compounded monthly. First I will define two more variables to make the 
calculations easier:
# J = monthly interest in decimal form = I / (12 x 100)
# N = number of months over which loan is amortized = L x 12

Okay now for the big monthly payment (M) formula, it is:

                          J
     M  =  P  x ------------------------

                  1  - ( 1 + J ) ^ -N

M = P * ( J / (1 - (1 + J) ** -N))

*/


function calcMonthlyPayment($amount, $int, $term)
{
     $I = $int;   /*I understand this piece was unnecessary however, it helped me keep my ducks in a row if you know what i mean :) */
     $J = $I/1200;
		 //amount of loan
     $P = $amount;
		 //Length of Note in months
     $N = $term * (-12);
		 //breaking the denominator up into pieces for order of operations
     $base = 1+$J;  

     $base = pow($base, $N);
     $base = 1 - $base;
		 //completing the formula
     $M = $P * ($J) / ($base);
     $M = number_format ($M, 2);

	    return $M;
}

$check = calcMonthlyPayment(200000, 5.78, 30);
echo "<p>$check</p>";
?>

Thanks for the help!

Warmaster

HalfaBee

I am pretty sure php knows how to do maths 😉
You just need to use brackets to make sure it is done in the correct order.

$M = $P * $J / (1 - pow(1+$J , $N ) );

laserlight

I basically had to break my formula down into small pieces based on the proper order of operations. Why can't I just put a whole formula in there and have php output the proper figures? Or is it a flaw with php?

It depends on the formula. Also, a complex formula might be easy to write down on paper, but without the vertical space afforded in the text of a program, it could become difficult to read, so breaking it into parts would enhance readability. Furthermore, a formula might have repeated parts, and calculating these separately and then reusing the result could be an optimisation.

Now, looking at the formula that you wish to implement, I'd say that you should use the names instead of the symbols. P, I and L are all very well when writing the formula down, but in code it would be simpler to just use the names that they represent.

For example, I might translate your given formula into:

function calcMonthlyPayment($principal, $annual_interest_rate, $term)
{
    $interest_rate = $annual_interest_rate / (12 * 100); // Monthly
    return $principal * ($interest_rate / (1 - pow(1 + $interest_rate, $term * 12)));
}

Warmaster

Sheesh, now that I feel completely stupid...

  $I = $int;
     $J = $I/1200;
		 //amount of loan
     $P = $amount;
		 //Length of Note in months
     $N = $term * (-12);

	 //HalfaBees version which works ::sheepish grin::

	 $M = $P * $J / (1 - pow(1+$J , $N ) );
	 $M = number_format($M, 2);

			return $M;

I know what I was doing wrong which obviously does return a different value. I separated out my pow() instead of using it within the brackets. I forgot about the fact that it completes inside the brackets first, then it will raise that to the appropriate power, then it takes that away from 1, instead I was doing it backwards. Oh well, lessons learned! Thanks HalfaBee!

edit- Thanks laserlight, that code looks much cleaner and it is easier to read. For the sake of the formula I was using, it was easier to just follow along with it as the symbols but I see what you mean and how that could be more beneficial, as well as aesthetic.

Warmaster