think about the bank. their system is with a minimal unit: 0.01, or, a cent. So any more decimal places would be rounded using the most common rule: 0-4, round down; 5-9, round up.
so think about the following two scenarios:
1. Bank lends 0.1 to A, charging 6.31% annually. This 0.1 comes from two resources, a 0.05 deposit from B and the left 0.05 deposit from C. The deposit rate, for simplicity, also assumed to be 6.31%. Then what would be left in the bank after one year?
Not zero. The correct answer would be: (RND means round the number)
RND{ 0.1 * ( 1 + 6.31% ) } - 2 * RND{ 0.05 * ( 1 + 6.31% ) } = 0.11 - 2 * 0.05 = 0.01
Well, you can say it's trivial. Who would give a damn to the 1 cent, especially for the bank. So let's see another example:
2. You have 160,000 to deposit into a bank with 3.14% annual deposit rate. What would you expect?
The answer may not be the most common one: 160,000 * ( 1 + 3.14% ) = 165,024. Let me show you another trick.
You split your money into pieces each with identical amount: 0.16. So for each piece, the finaly amount after a year would be RND{ 0.16 * ( 1 + 3.14% ) } = 0.17. Thus you would get 0.17 * 10^6 = 170,000. Compared with previous 165,024. An extra 4,976 is in your pocket. And that equals to a 6.25% annual rate.
Of course, there are many limits in the bank. And my example is not to teach you to arbitrage, but to show you how a badly designed system could damage.
I won't bother to explain the math after the two examples. Just for fun.
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