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I have just purchased a 12c calc. I am having trouble with one particular par t of TMV calculations. When I am trying to figure out n (number of years) the calculator automatically rounds up to the next higher number. I understand why it does this with certain applications of TMV but I need it to display actual time. For instance I am trying to figure out how much time it takes to get to a FV when I have a specific PV and interest rate. It always round the number to the next highest year. Is there a way to get the calculator to display actual years (3.02 years)???

No. Sorry.

The users guide has a procedure you can use to estimate the fractional part of n. It is found on pages 63 through 68.

This was a design choice made by the original 12c team long long ago.

The 12-C can't do this with the built-in TVM functions, but your specific problem seems easy to solve.

I believe the simple formula for compound interest is:

FV = PV * (1 + i) ^ n

Here n is the number of periods, and i is the interest rate per period expressed as a decimal. So 6% annual interest (compounded annually) gives:

FV = PV * (1.06) ^ n

If you want to do monthly compounding, divide the .06 by 12, and multiply n by 12.

Now using logarithms we can solve for the exponent n.

ln(FV) = ln (PV * (1.06) ^ n) = n * ln (PV * (1.06)) so

n = ln (FV) / ln (PV * (1.06))

Hope I didn't mess up my formula, algebra, or explanation too badly.

n=ln(FV/PV)/ln(1.06) ?

You're right, Tony.

The PV isn't part of the value raised to the power of n, so your solution is correct. Thanks!

Thanks guys,

You are right on the equation. I know that is one way to do it ( I was a math major) I was just curious if the 12c could do that function for me. Thank you all for a good speedy response.

FWIW, Neither the 17bii nor the 48G TVM solvers have the 12C rounding issue.

Edited: 24 Jan 2008, 8:37 p.m.

(* 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

Hi Gene,

I just tested your last example on my 17BII+, the answer for N it returns is 44.74. Any idea why?

Gene,

I think you've meant "monthly" ;-)

Quote:
How many annual deposits of $100 does it take ...

Best regards,

Peter A. Gebhardt

Edited: 25 Jan 2008, 4:43 a.m.

Brandony,

Pls. be aware that so called "Usances" (usages or special regulations for the calculation of interest) exist in different jurisdictions and/or for different financial instruments.

As a reference look at:

http://en.wikipedia.org/wiki/Compound_interest

were exceptions are described, where and when to use "simple interest" calculations.

So the implementation of TVM in the HP-12c makes perfectly sense for someone used to divide the total accumulated interest into interest from periods with compounded and such of simple interest respectively.

Wether if it's easier to calculate the simple interest part by the HP-12c method or from the fractional result of the HP-17b (and its siblings) is left to anybody's preference.

Best regards

Peter A. Gebhardt

Edited: 25 Jan 2008, 9:42 a.m.

Oops. Bad day for me all around. :-)

The 17b2+ returns the mathematically correct value for N.

It solves for N differently than the 12c.

How about the 48G+ ?

No need to search any longer.

The 12c designers took the practical approach. Doesn't seem to have hurt sales over the last 25 years. :-)