The "rounding" issue Message #8 Posted by Gene Wright on 24 Jan 2008, 9:44 p.m., in response to message #7 by allen
(* Edited to correct to monthly example rather than annual *)
An exact value for N in these circumstances may be mathematically correct, but meaningless in reality.
For example, the question: How many MONTHLY deposits of $100 does it take into an account paying 6% compounded monthly before you have accumulated $5,000? (Assuming payments made at the end of a period.
The exact answer for N that many calculators give is 44.7402....
However, the real answer is that it takes 45 deposits of $100 under these circumstances.
You can't have .7402 of a $100 deposit. You either make a deposit of $100 or you don't.
After 44 deposits, you would have less than $5,000. At 45, you have more than $5,000. No integer number of deposits will give you exactly $5,000.
Therein lies the problem. 44.74... makes the formula work to equal the $5,000, but, IMO, it is a malformed question.
The 12c designers choose the "real" approach.
Other calculator models (and manufacturers) choose the mathematically correct solution.
That is why the confusion exists.
When I teach this type of stuff at the university, I usually pose the questions like this: "How many deposits...before you would have at least $5,000 in the account?"
The answer would be 45 in this set of circumstances. 44.74... if returned would be rounded up by thinking the issue through.
My 2 cents (which doesn't buy much these days)
Gene
Edited: 25 Jan 2008, 8:09 a.m. after one or more responses were posted
