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As the question states, is there a way to find precision used based on margin of error in compound interest problem?

The question is based off the following scenario: A financial system that projects APY of a given certificate principal amount and interest rate along with the formula to solve it along can easily give the future value of the certificate. The problem; there is not a hard convention on the number of decimal places and the rounding method in which the system uses to compound. The problem I am running into is when I calculate it manually, I always seem to be pennies off from what the system projects. The problem is further complicated by inherit problems with the type of data used by the system (floating data types are known to produce inaccuracies). Still, it would take forever trying all the different combination of methods it could be; 2 decimal places rounded up, 4 decimal places truncated, 3 decimal places rounded down, etc. Thanks in advance.

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I think a definite answer to your question, at least from a mathematician, will be very difficult to obtain. The mathematical formulae for time-value calculations do not have any inherent rounding - if the interest rate is strictly constant and the financial institution doesn't round, the value of a CD will be precsiely what the formula spits out.

The discrepancy in your problem can be chalked up precisely to your question - the calculator you used to find the APY assumed some degree of rounding. However, without knowing specifically what system that was and given (as you said) that there is no real convention in place, I fail to see how anyone would be able to tell you the specific round scheme your particular calculator used. It may round up in every compounding period, carry out operations to some finite precision, use precalculated (and thus finite precision) interest factor tables, etc.

The point is, without more information on your calculations and the specific system you used, the is very little anyone can tell you about how precisely your system handles rounding...

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Thank you. You pretty much confirmed my thoughts on it. :) – hydroparadise Dec 1 '11 at 13:33

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