(* 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*