Creating an inflation calculator in PHP

Question

Heres the code I have at the moment, its all working as intended, however, the cumulative total isn't working, and I'm positive I'm doing something absolutely stupid.

assume period = 20
assume inflation = 3
assume nightlycost = 100
assume nights = 7

$yearlycost = $nightlycost*$nights;
while ($period > 0) {
    $period = $period-1;
    $yearlyincrease = ($inflation / 100) * $yearlycost;
    $nightlyincrease = ($inflation / 100) * $nightlycost;
    $nightlycost = $nightlycost + $nightlyincrease;
    $yearlycost = ($yearlycost + $yearlyincrease) + $yearlycost;
}

Result:
Nightly Hotel Rate in 20 years: $180.61 - <?php echo round($nightlycost, 2); ?> correct

Weekly Hotel Rate in 20 years: $1264.27 - <?php echo round($nightlycost, 2) * 7; ?> correct

Total cost to you over 20 years: $988595884.74 - <?php echo round($yearlycost, 2); ?> incorrect

Everything outputs correctly and as expected, except for the yearly cumulative cost. It should take the previous yearly cost and add that years cost+inflation.

Example: first year is 700, so second year should be 700 + 700 + 21 (21 is 3%, the inflation for that year). Second year cumulative total is thus: 1421. Third year will be 1421 + 721 (last years total) + 3% of 721.

Hopefully this is clear enough for you to see where I'm going wrong. Thanks!

Answer 1

I find it hard to understand where your code goes wrong, but my intuition is that the last line in your loop body should have a multiplication.

Basically, you have a base cost for period 0. Then you want to calculate the cumulative cost given inflation after X years. That cost is (pseudocode)

base = nightlycost + nights
infl = 1.03
cumulative = base + base*infl + base*infl^2 + base*infl^3 + ... + base*infl^periods

The last expression can be simplified to

cumulative = base*((1-infl^periods)/(1-infl))

(This holds according to Eq. 4 here: http://mathworld.wolfram.com/ExponentialSumFormulas.html)

Example:

$base = 100*7;
$infl = 1.03; // 3% of inflation/year

$periods = 2;
$cumulative = $base * (1-pow($infl, $periods))/(1-$infl);
print "Cumulative cost after $periods is $cumulative\n";

// Let's try with three periods.
$periods = 3;
$cumulative = $base * (1-pow($infl, $periods))/(1-$infl);
print "Cumulative cost after $periods is $cumulative\n";

Output:

Cumulative cost after 2 is 1421
Cumulative cost after 3 is 2163.63