HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation (5936 Views)
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Message 1 of 20 (5,936 Views)

# HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Hello. I am preparing for FRM certification, and the study guide warns me of a following error produced by the HP 12c.
This is the question : if 5000 USD is invested in a fund offering a rate of return of 12 %, approximately how many years will it take for the investment to reach 10000 USD ?
Answers : a) 4 years b) 5 years c) 6 years d) 7 years

If you do this with your HP 12c : PV = -5000, FV = 1000, i=12, pmt=0, ->n, the result is : 7

However the exact result is 6.12.

The study guide tells me : One problem with the HP12C is that is does not have the capability to round. In this particular question, you will come up with 7, although the correct answer is 6.1163, therefore you must answer c) 6 years in the quiz.

I would like to know in what type of situations does the HP12C generate this error ? Only when trying to find out the implied n ?
When do I not trust the result given by my calculator ???

Thanks for your help.
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Registered: ‎01-16-2007
Message 2 of 20 (5,936 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

[ Edited ]

Hello,

this has been discussed a couple of times in the past how and why the 12c is working this way.

This is not a problem of the calculator, it is a financial problem and requires the understanding of cash flows (which is not that hard ;-).

The exact result of 6.12 is a mathematical solution whereas in the financial solution you can not have a 0.12 payment, there are only full payments.

So after 6 years you have a sum of 9869.11 and the question is when will the investment reach 10000.00 which would require an additional payment and that is the reason why the 12c gives you 7.

Also I believe that the answer your test requires is wrong, the correct answer is indeed 7 but recent history has shown that especially the banks in the U.S do not care so much for numbers anymore. Lehman Brothers just jumps into my mind.

> When do I not trust the result given by my
> calculator ???
Never trust a stupid machine which can only count very quickly. If in doubt, use your brain. ThatÂ´s what it is for ;-)

HTH,
Andreas

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Message 3 of 20 (5,881 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Cyril,

Don't let anyone tell you this is anything but an error, because  it is an error and should be corrected by HP.  The question isn't how many full payments are required to get to \$12,000- that indeed would be 7.  The question is how many years would it take and that indeed would be 6.12 years.  If you make this calculation on the HP 12C instead of the HP Platinum 12C you get your 6.12 years.  There is nothing wrong or awkward about a fractional answer.  Suppose you were calculating a breakeven period for financial cash flows?  A breakeven period of 6.12 years is quite a bit different than one of 7.0 years.

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Message 4 of 20 (5,875 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

It is not an error, but rather the way you interpret the question, and how you interpret financial rules. You *also* will get 7 on the 12c.

This is also the reason that on exams like the CFA you specify whether you are using a 12c/12cp for the exam. If you are, the correct answer for this question is 7. If you are using another calculator that doesn't apply this rule in this way and gives the fractional result, then 6 is the correct answer.

This is like saying that 0^0=1 or 0^0=?. Depending on how you interpret it, and what it is being used for, it can be multiple things.

--

TW

Although I work for the HP calculator group, the views and comments expressed here are my own.
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Registered: ‎02-09-2009
Message 5 of 20 (5,870 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Hi!, all:

In the next site, have a many examples of use, HP12C Platinum.

http://www.educalc.net/149642.page

Best Regards.

MACH.:smileyhappy:

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Registered: ‎02-04-2010
Message 6 of 20 (5,861 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

I would say the correct answer is 7.

It depends on whether the interest payments are made monthly or annually. The question does not pecify, but if interest is payed annually and compounded annually then if you withdrew the money at any time before the 7 year mark, you would NOT get \$10,000. So you have to wait till n=7. The fact that you get more than \$10,000 then is a bonus, but you'll get less than \$10,000 at any time before.

If interest is payed monthly and compounded annually, it would take 6y 2m to reach \$10,000, which is 6.16666' decimal.

If interest is payed monthly and compounded monthly, it would take 5y 10m to reach \$10,000, which is 5.83333' decimal.

In any case, 6.12 is wrong unless interest is payed in small enough increments for that resolution (and compounded annually). It would depend on what your financial institution is offering.

This is my opinion and I'm an engineer, not a financial guru. Perhaps hpgene can shed more light on this.

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Message 7 of 20 (5,829 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Interesting.

With the 12C the answer is indeed 7 but if you then request the FV you will get 11,053.41 and not 10,000. I would prefer to see the real answer 6.12 years and decide by myself if the correct answer is approximately 6 or 7 years.

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Message 8 of 20 (5,527 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

The 12c (and 12c platinum) are "per period" calculators. That is, they work with interest rates per period. This is different than the HP 10bII approach (and that nameless TI competitor) which have the user set the number of periods per year.

Because of that, the interest rate is always entered as a periodic interest rate.

Because of that, n is entered as the number of periods.

If you are dealing with years, where payments are made each year and interest is accrued each year, you cannot have a fractional year. Can't be done. So, the designers of the 12c about 30 years ago had a choice...

When computing n do we

a) give the "mathematical" answer that is correct but has no correspondence to anything in reality (that's what the 6.12 is)?

b) give the number of periods when you have at least the value in the FV for the first time (that's what the answer of 7 is)?

or

c) give the number of periods just before you have the value in the FV (which would be an answer of 6)?

Now, let me tell you that I taught business math at the college level for 20 years using both types of calculators. Students easily understood the distinction once they thought about it and weren't just writing down a number their calculators gave them.

Example:

Teacher: Annual compounding and annual payments. How long until you have \$10,000?

Student: My calculator shows 6.12

Teacher: Ok, what happens if you try to go get your money at 6.12, since it is annual compounding and annual payments?

Student: Uh, hey... I can't do that can I?

Teacher: No. So when do you first have \$10,000?

Student: At the 7th period.

Student B: Hey, I have a Hewlett Packard 12c calculator and it already gave me the answer of 7.

Teacher: I see that although you are Student B you will probably get an A.

:-)

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Message 9 of 20 (5,108 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Not sure I can continue using the calculator because of this; although I must say in practice, I don't think the number of periods is what I'm going to focus on.

To elaborate on the mentioned example:

if 5000 USD is invested in a fund offering a rate of return of 12 %, approximately how many years will it take for the investment to reach 10000 USD ?
Answers : a) 4 years b) 5 years c) 6 years d) 7 years

Assuming the investment compounds annually, then it is 7 years for the already discussed reasons.

If a loan repayment problem is addressed "n" depends what to do with the extra.  If the extra is .2, then the last payment may be balloned.  If the extra is .8, then it may be added to the next payment.

This should have been something that the user should judge, not the calculator.

Lets look at this question which gives out the wrong answer.  If anyone can explain this let me know.

At 8% annual interest, how long would it take for \$1 to turn to \$4.   The calculator results in 19 periods.  With 19 periods, the investment grows to \$4.3.  With 18 periods, the result is \$4.  Why did the calculator round this result up?

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Message 10 of 20 (5,104 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Actually I just found an actuarial program, which will take some time putting into the calculator, that I think will work.  http://h10025.www1.hp.com/ewfrf/wc/document?docname=bpia5043&cc=us&dlc=en&lc=en&jumpid=reg_R1002_USE...

Will try to let everyone know how it turns out.

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Message 11 of 20 (4,899 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

[ Edited ]

Committing to memory the formulas for time value of money can prove to be useful, even if you use a financial calculator.   If you really need to get the exact N on the 12c/12cp, then it wouldn't be too difficult this way.  I think it might be easier than entering in a program.

FV = PV(1+i)^n

10000 = 5000 (1 + .12)^n

2 = 1.12^n

LN2 = LN1.12 *n

.69315 = .11333 * n

6.11621 = n

You can also solve for i using the formula:

10000 = 5000 (1 + i)^ 6.11621

2 = (1 + i)^6.11621

LN2 = LN(1 + i) * 6.11621

.69315/6.11621 = LN(1 + i)

.11333 = LN(1 + i)

e^.11333 = 1 + i

1.12 =1 + i

.12 = i

Let's use your example now.

"At 8% annual interest, how long would it take for \$1 to turn to \$4.   The calculator results in 19 periods.  With 19 periods, the investment grows to \$4.3.  With 18 periods, the result is \$4.  Why did the calculator round this result up?"

4 = 1 (1+.08)^n

4 = 1.08^n

LN4 / LN1.08 = n

18.01294 = n

hpgene and Tim both have good explanations for the 12c/12cp behaviors in this regard.

Hope this helps,

Markoose

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Message 12 of 20 (4,888 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Um, actually, it's only \$4 if the amount is to be recorded in dollars and cents. Suppose that the question were with regard to a deposit of \$10,000 turning into \$40,000? Then at the end of 4 years, the amount with compounded interest would be \$39,960.20 (rounding up the the nearest whole penny). I'm sure the HP 12c would show this if one entered the PV(1+i)^n as Markoose correctly stated it, using n=18.012937 (the solution to Ln[4]/Ln[1.08]).

Round-off's a funny thing, and it particularly shows when computing with logarithms. For example, in the original problem, Markoose's calculator gave a result of 6.11621 years; Mathematica gives 6.1162554 years. Which answer is most correct? Well, even if you're dealing with hourly interest the results are about the same: it's a difference of 23.88 minutes' worth of interest.

We're back to the question of understanding the problem, its underlying mathematics, and its real-world interpretation. For some statement of the problem, each of the calculators is correct; with a different interpretation, each can be wrong, sans question!  The problems that started this discussion were not precisely stated as the surrounding assumptions were missing. I would say "shame of the test-writing organisation," but then I'd also flunk the exam were I to misread the questions.

Anyway, it's not the calculator that gets certified: it's its operator!

--Leopold Bloom

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Message 13 of 20 (4,885 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

[ Edited ]

LeopoldBloom wrote:

Um, actually, it's only \$4 if the amount is to be recorded in dollars and cents. Suppose that the question were with regard to a deposit of \$10,000 turning into \$40,000? Then at the end of 4 years, the amount with compounded interest would be \$39,960.20 (rounding up the the nearest whole penny). I'm sure the HP 12c would show this if one entered the PV(1+i)^n as Markoose correctly stated it, using n=18.012937 (the solution to Ln[4]/Ln[1.08]).

Round-off's a funny thing, and it particularly shows when computing with logarithms. For example, in the original problem, Markoose's calculator gave a result of 6.11621 years; Mathematica gives 6.1162554 years. Which answer is most correct? Well, even if you're dealing with hourly interest the results are about the same: it's a difference of 23.88 minutes' worth of interest.

We're back to the question of understanding the problem, its underlying mathematics, and its real-world interpretation. For some statement of the problem, each of the calculators is correct; with a different interpretation, each can be wrong, sans question!  The problems that started this discussion were not precisely stated as the surrounding assumptions were missing. I would say "shame of the test-writing organisation," but then I'd also flunk the exam were I to misread the questions.

Anyway, it's not the calculator that gets certified: it's its operator!

--Leopold Bloom

Actually, with full precision and not using limited reentry, my calculator gives an answer of 6.1162553742 for n. This is an exact response and seems to agree closely with Mathematica.

The problem was that I had my calculator set at fix 5 and I reentered the numbers manually instead of letting the calculator's internal precision carry the numbers through the calculation.  Don't ask me why I solved it this way the first time around.

I will not edit my previous post, but I will show the keystrokes I used on the 30b when I calculated it a second time.

10000

input

5000

/

shift 4  (LN)

1.12

shift 4

/

Again, my result was 6.1162553742

Regards,

Markoose

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Message 14 of 20 (4,877 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Yes the acturial program works well and is simple to operate.  I'm using the n program and am satisfied for now.

Regular Advisor
Posts: 90
Registered: ‎09-18-2010
Message 15 of 20 (4,874 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Thanks for your quick reply, Markoose!

I wasn't trying to criticise Markoose's calculator's precision so much as to indicate that for problems of this kind one needs to be judicious in its use. I just set up the problem for Mathematica to the same precision as his HP 30b used, and got an identical result (as expected). Generally, I frequently use an HP 30b feature to see what the internal precision is: simply touch the backspace key and it shows in all its glory. Further, you can use the backspace key to adjust the internal precision for consequent calculations using the now stored number. It's a nice feature!

Numerical analysts are quite concerned over precision and round-off errors, and they understand the phenomena far better than I want or generally need to. It appears to me that the HP 30b is quite admirably set up for problems of this kind -- as evidently are the HP 12c and 12cp.

--Leopold Bloom

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Registered: ‎09-14-2010
Message 16 of 20 (4,866 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

jarrun79 wrote:

Yes the acturial program works well and is simple to operate.  I'm using the n program and am satisfied for now.

I'm glad to hear that.  I only offered using the formula as a simpler (in my opinion) alternative.

Markoose

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Posts: 74
Registered: ‎09-14-2010
Message 17 of 20 (4,865 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

LeopoldBloom wrote:

Thanks for your quick reply, Markoose!

I wasn't trying to criticise Markoose's calculator's precision so much as to indicate that for problems of this kind one needs to be judicious in its use. I just set up the problem for Mathematica to the same precision as his HP 30b used, and got an identical result (as expected). Generally, I frequently use an HP 30b feature to see what the internal precision is: simply touch the backspace key and it shows in all its glory. Further, you can use the backspace key to adjust the internal precision for consequent calculations using the now stored number. It's a nice feature!

Numerical analysts are quite concerned over precision and round-off errors, and they understand the phenomena far better than I want or generally need to. It appears to me that the HP 30b is quite admirably set up for problems of this kind -- as evidently are the HP 12c and 12cp.

--Leopold Bloom

Leopold,

I didn't think you were trying to criticize my calculator's precision.  I do recognize, however, that I was clumsy in my approach and felt that I did the 30b no justice.  I find that it is amazingly accurate and feel kind of dumb that I would reenter the numbers instead of following through the calculations.  Then again, I was doing the calculation while typing out solution to the formula on my message.

Like you, I really like the backspace key.  It is very useful since I fix my digits at 5.  If I set it to float (FIX -1), then I get more numbers than I would like to see.  :smileyvery-happy:

Regards,

Markoose

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Posts: 90
Registered: ‎09-18-2010
Message 18 of 20 (4,806 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Very early in this discussion, Andreas Möller observed that the HP 12c produces the correct result of 7 years for the practical application of when one could actually collect the principal and interest from a bank, as compared to the theoretical question of when the sum would actually reach 10000.00.

For what it's worth, the HP 30b has a similar anomaly in computing TVM when the period of compounding is not identical to the period of making payments. Indeed, in the string for "TVM Question on HP 30b (q.v.), it appears that the principal and interest are actually posted each month in a problem with monthly payments and quarterly compounding.

Here, too, the real question of when a formula gives an accumulated result as opposed to when one can actually collect that amount is the matter for interpretation. One would hope that examiners would pose their questions precisely lest the folk taking the test produce the wrong correct answer!

--Leopold Bloom

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Message 19 of 20 (3,555 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

Why doesn't HP simply offer the rounding when it's in RPN mode on the 12 C platinum. But then allow for the fractional answer on the algebraic mode?  The rounding is accurate when you're solving for the number of periods. But the fractional answer is correct as well. It's a calculator... can't someone just add that small function so that all these people aren't frustrated?  It seems like such a simple answer. In all fairness it frustrates me to. I can get the fractional answer but I have to go through a lot more process. And the purpose of having the calculator is to shorten that process. What do you say...  Is there any hope HP will ever help those people who are looking for the fractional answer on the 12c?  And granted I understand that the 10b the 20b and all those calculators do offer the fractional answer. But let's face it the 12 C is an easier calculator to use and has more functions. And most importantly it is a cooler calculator because it is horizontal instead of vertical in design.

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Registered: ‎02-09-2009
Message 20 of 20 (3,550 Views)

# Re: HP 12c Platinum rounding error in computing n on a PV/PMT/FV calculation

[ Edited ]

Hi!, Bigdaddymolina:

Maybe you can understand, how the HP12CP, looking at the learning modules, you can download from ... http://h20331.www2.hp.com/Hpsub/cache/300065-0-0-225-121.html

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