TVM inaccuracy  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: TVM inaccuracy (/thread40294.html) 
TVM inaccuracy  Thomas Radtke  08112003 Hi, am I the only user who finds the TVM calculations on HP18C et al. to be horribly inaccurate? Take just a simple example: PV=100, PMT=10, I%YR=3, annual interest compounding, monthly payments. Interest conversion leads to I%=2.96... and the subsequent TVM calculation (Begin mode, N=12, P%Y=12) gives a value of 224,941194... where it should be exactly 224.95. Higher cash flows lead to a worser inaccuracy. Are these problems accepted? Any statements are very welcome. Thanks,
Thomas
Re: TVM inaccuracy  Gene  08112003 Original 12c gives $224.9411945 Excel 2000 gives $224.941194069285 Where did you find that the "exact" answer should be $224.95?
Probably due to some rounding in the interest rate conversion. i is equal to 0.00246626977230369 and 0.00246627 on the 12c.
Re: TVM inaccuracy  Thomas Radtke  08112003 Hi Gene,
1) I can do this by hand:) Well all three methods get the same result. That, of course, does not mean that I'm right;). Might be bad logic on my side. Anyway I will look into this further and if only to prove that I'm too stupid to use my pencil and calculators;(. Thanks for your answer!
Thomas
Re: TVM inaccuracy  Gene  08112003 Well, perhaps what you're using is not really a simple example? You have a rate that is annual and monthly payments. Usually, simple problems have a rate and payment frequency that are the same. On the 12c, here's what I do to find the given answer:
1.03 ENTER 12 1/x Y^x 1  100 x i (This gives the equivalent interest rate per month, or 0.246627, which means that 2.959524% compounded monthly is equivalent to 3% compounded annually)
which returns the value I have posted earlier.
Re: TVM inaccuracy  Victor Koechli  08132003 This is really interesting. If you supply the FV value you state as exact and calculate i, you get 2.96473629127 (on the 48GX) which is significantly different from the 2.959523724 you get from the conversion. If you add interests up manually you do indeed get 224.95. I get this result by doing
11 10 and adding 3 for the interest from the initial 100. What's going on here? The error seems too large to be simple roundoff...
Cheers, Victor
Re: TVM inaccuracy  Tony  08142003 Very interesting Victor!! So, that is where the exact 224.95 comes from. It uses simple interest over the year!! As you say : 224.95 = 100*1.03 + 12*10 + .03*10*6.5 TVM uses compound interest, like so:
100*1.03 + [10*.03*(1.03)^(1/12)]/[(1.03)^(1/12)  1]
Re: TVM inaccuracy  Victor Koechli  08142003 Hmmm... Forgive my ignorance, but I'm trying to find out why this makes a difference. Is it because, in this example, interest is only compounded once a year, while payments are received monthly? And if so, could you still calculate this example using the TVM solver?
Cheeers, Re: TVM inaccuracy  Tony  08142003 >Hmmm... Forgive my ignorance, but I'm trying to find out why this makes a difference. Oh, I just gave the mathematical side. My reading was you wanted to know why there was a small difference.
The TVM expression I gave assumes monthly compounding. > Is it because, in this example, interest is only compounded once a year, while payments are received monthly? The exact 224.95 answer assumes the payments get simple interest. If the plan lasts for one year only then there is really no compounding at all. >And if so, could you still calculate this example using the TVM solver?
No, TVM will not do this. But what it will do is ... if the savings plan lasts for a number of years, and the compounding occurs one a year, then you can compute an FV by using the equivalent endofyear payment, as PMT. This would be This also works with n=1, of course, but we have had to calculate the PMT manually... this is as close as we can get to representing this problem in TVM. Hope this ramble helps :)
Cheers, tony
Re: TVM inaccuracy  Thomas Radtke  08142003 Hi Tony, Victor, Gene, I've got the solution to this problem already. I'm in the process of publishing a paper about it and as soon as it is accepted, I will report here all findings. Please understand that I want to get this damn thing out first as I really need it (beeing unemployed for a too long time now, this is good stuff to present to any potential employer). Btw., HP, TI et al., any vacancy for a good physicist w/ PhD?:).
Thomas
