TVM inaccuracy

[Thomas Radtke]

Hi,

am I the only user who finds the TVM calculations on HP-18C 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

[Gene]

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.

[Thomas Radtke]

Hi Gene,

1) I can do this by hand:)
2) I wrote an iteration for my 32SII
3) I solved the iteration to get an analyical equation. Thats probably more exact since there is not such a high exponentiation necessary as in the usual formula which explicitly needs the conversion (you end up w/ e.g. q^N^CP, CP=compound period, something like that). Dunno exactly, I haven't done the error calculation yet but am fairly sure that this method is problematic.

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

[Gene]

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)
100 PV
10 PMT
12 N
FV

which returns the value I have posted earlier.

[Victor Koechli]

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

10*.03 + 10*--*.03 + 10*--*.03 + ...

            12          12

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

[Tony]

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]

[Victor Koechli]

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,
Victor

[Tony]

>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.
TVM always compounds at each payment incident.

> 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 end-of-year payment, as PMT. This would be
121.95 in this case. So you can correctly compute the FV after 10 years with n=10 i=3 PV=100 PMT=121.95 at END.

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

[Thomas Radtke]

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