The Museum of HP Calculators

HP Forum Archive 18

 HP 12c Platinum TMV helpMessage #1 Posted by Brandony on 24 Jan 2008, 3:36 p.m. 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)???

 Re: HP 12c Platinum TMV helpMessage #2 Posted by Gene Wright on 24 Jan 2008, 3:56 p.m.,in response to message #1 by Brandony 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.

 Re: HP 12c Platinum TMV helpMessage #3 Posted by Steve Perkins on 24 Jan 2008, 6:26 p.m.,in response to message #2 by Gene Wright 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.

 Re: HP 12c Platinum TMV helpMessage #4 Posted by tony (nz) on 24 Jan 2008, 6:58 p.m.,in response to message #3 by Steve Perkins n=ln(FV/PV)/ln(1.06) ?

 Re: HP 12c Platinum TMV helpMessage #5 Posted by Steve Perkins on 24 Jan 2008, 7:25 p.m.,in response to message #4 by tony (nz) You're right, Tony. The PV isn't part of the value raised to the power of n, so your solution is correct. Thanks!

 Re: HP 12c Platinum TMV helpMessage #6 Posted by Brandony on 24 Jan 2008, 7:41 p.m.,in response to message #5 by Steve Perkins 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.

 Neither the 17bii nor the 48G TVM solvers have the 12C rounding issue. Message #7 Posted by allen on 24 Jan 2008, 8:19 p.m.,in response to message #1 by Brandony FWIW, Neither the 17bii nor the 48G TVM solvers have the 12C rounding issue. Edited: 24 Jan 2008, 8:37 p.m.

 The "rounding" issueMessage #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

 Re: The "rounding" issueMessage #9 Posted by Kareem Mokdad on 25 Jan 2008, 3:37 a.m.,in response to message #8 by Gene Wright Hi Gene, I just tested your last example on my 17BII+, the answer for N it returns is 44.74. Any idea why?

 Re: The "rounding" issueMessage #10 Posted by Gene Wright on 25 Jan 2008, 8:10 a.m.,in response to message #9 by Kareem Mokdad The 17b2+ returns the mathematically correct value for N. It solves for N differently than the 12c.

 Re: The "rounding" issueMessage #11 Posted by Peter A. Gebhardt on 25 Jan 2008, 4:41 a.m.,in response to message #8 by Gene Wright 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.

 Re: The "rounding" issueMessage #12 Posted by Gene Wright on 25 Jan 2008, 8:08 a.m.,in response to message #11 by Peter A. Gebhardt Oops. Bad day for me all around. :-)

 Re: Neither the 17bii nor the 48G TVM solvers have the 12C rounding issue. Message #13 Posted by Mad Dog ebaycalcnut on 26 Jan 2008, 5:29 p.m.,in response to message #7 by allen How about the 48G+ ?

 The ONLY one that does this is the 12cMessage #14 Posted by Gene Wright on 26 Jan 2008, 8:50 p.m.,in response to message #13 by Mad Dog ebaycalcnut 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. :-)

 Re: HP 12c Platinum TMV helpMessage #15 Posted by Peter A. Gebhardt on 25 Jan 2008, 6:31 a.m.,in response to message #1 by Brandony 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: 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.

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