To make something run automatically, you'll need a program like crontab. If you are on Windows, you can use WinCron.
To multiply their money by a certain percentage, you'll have to know a little math. A percentage is a part of a whole. Assuming the whole of someone's money is equal to 1, then the percent of their money is going to be a decimal, or something smaller than 1 (unless the percentage is higher than 100%). Therefore, we can assume that 50 percent is equal to .50, which is one-half of 1.
Since this is sort of a bank, you will need to know the absolute value of certain accounts, which means down to the fraction of a cent. For this, we are going to use a float. A float is a variable which is not truncated, and can be quite long. A float is usually about 14 digits long. It is 64 bit IEEE format. You may also hear a float called a double, or, in its mathematical sense, any real number.
We can assume that money will be variable, and therefore will be stored in a variable. In order to make a variable into a percent of a float, we'll have to multiply the variable by the percent. Let us assume the percent is 15%, for this example:
$money = (float)($money * .15);
This will set $money to 15 percent of its original value. If you want to add 15 percent, this makes the whole 1.15, or 115%, rather than 1 (100%):
$money = (float)($money * 1.15);
This is the same as multiplying and then adding the original:
$money = (float)($money+(float)($money * .15));
As for the stock exchange, I have no idea how to do this, but you'll need to have it update often, which is another cron job.
Hope this helps.