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adamyoung1983
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PV Pension - HP 10bII getting different answer than HP 12c - PLEASE HELP TEST ON MONDAY

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Calculating for PV of monthly payments:

PMT = 1,200

n = 198.72

i = .41667

FV = 0

 

Calculators are set to Begin mode and 1 P/YR.

 

Answers:

10bII = 162,624

12c = 161,759 (book says this is the right answer)

 

Why is the 10bII not getting the same answer?

 

P.s. I have reset the 10bII calculator and still no luck.

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Joe_Horn
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First you say "monthly payments" but then you say "1 P/YR". Which is it: twelve payments per year, or one payment per year? One payment per year with N=198.72 is an impossible scenario, but if it's monthly, then P/YR should be 12, not 1.

 

You say i=0.41667 ... but that's a strange annual percentage rate. It looks more like a MONTHLY rate. If so, the annual rate is 5%, and the rate must be input differently on both machines: 5 [I/YR] on the 10bII, and 0.41667 [i] on the 12C, or even better, 5 [g] [i].

 

Also, the HP-10bII and HP-12C treat N differently.  The 10bII allows fractional values for N, but the 12C only allows whole number values for N. When you say N=198.72, what do you mean by "198.72 payments"? 198 equal payments followed by a final smaller payment?

 

Disclaimer: I don't work for HP. I'm just another HP calculator user.

-Joe-
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adamyoung1983
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Thanks for the response. I’m afraid I don’t have a good answer to your comments. These values are how the answer in the back of the book reflects how it should be input on the 12C. I tested it with my colleagues 12C and it produced the answer given. When replicated on the 10bII it was a few dollars off, which is bothersome.
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David_M
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I agree with Joe that the stipulation of 1 period per year doesn't seem realistic for a problem like this, since it implies that the full term of the pension in question is close to 200 years.  And while it could simply be a coincidence, an interest rate of 0.41667 seems suspiciously close to 5/12, which would be reasonable for a monthly effective rate of a 5% APR.

Even if we ignore the above and just assume that the extra-terrestrial retiree in question has a 260+ year life expectancy and the pension has a 5/12% APR with 1P/YR, the 12c and 10bII handle periods with fractional values differently.  In particular, the 12c appears to treat the fractional part of the period as an "odd period" calculation, while other HP calculators that I've tried (17BII, 30b, 50g, Prime [emulator], 10bII+ [emulator]) simply use the period given in the standard TVM formulas. (Reference: page 186 of the "HP 12c Financial Calculator User's Guide", where the actual formula used by the 12c is noted as "compound interest/with simple interest used for an odd period".)

It's possible to get the same answer from your 10bII, but it requires some additional steps to mimic the handling of the odd period on the 12c.  You start by solving for the PV using only the integer part of the periods:

BEGIN MODE

P/YR: 1
n: 198
i: 0.41667
PMT: 1200
FV: 0
Solve for PV: -162244.568781

Now determine the odd period factor.  This is done by multiplying the interest rate by the fractional period, then adding 1.  It's important to remember that the interest rate here needs to be converted to its true decimal form by dividing it by 100 before adding the 1.  We actually need to divide the PV found above by this result, and to make things easier to calculate on the 10bII I'll multiply by the reciprocal instead.

RCL I/YR (0.41667)
÷ 100 = (0.0041667)
x 0.72 = (0.003000024)
+ 1 = (1.003000024)
1/x (0.997008949)
x RCL PV = (-161759.287038)

When I use the following input on my 12c (and 12c 30th Anniversary Edition), I get the following result:

BEGIN MODE

CLEAR FIN
n: 198.72
i: 0.41667
PMT: 1200
FV: 0 (not strictly needed since it was cleared above)
Solve for PV: -161759.2870

I've tried the same steps with a variety of different values for n, i, and PMT, and the above seems to work with each one.  There may in fact be an easier way to do this on the 10bII, as I'm no expert in the various modes and functions it provides (I don't own one).  But I believe the above provides consistent results when compared to a 12c used with similar input.

 

Just curious: what textbook has this problem?

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adamyoung1983
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When I first read the answer I also thought it was weird. I originally was using 12 P/YR but was way off from the answer. My wife told me just to try 1 P/YR and I got much closer. 

 

The question comes from the study book for the CDFA certification: The Financial Issues of Divorce - Module Two. I have typed out the full question below verbatim from the book. It is 2 parts to get to the final answer. The 1st part is what we have been discussing. You have to get it so that you can then use it as the FV in the second calculation to get the final answer which is A).

 

Question:

Nicole, age 48, has been married to Andy for 12 years and has worked for her current company for 19 years. She has received a statement from her company stating that based upon her current years of service and income, she is eligible to receive $1,900 per month at age 65 from her defined benefit plan. Assuming an interest rate of 5%, what is the present value of the marital portion of her plan?

 

A) $70,575

B) $111,744

C) $161,759

D $256,119

 

Answer:

Begin with 12/19 or 63% of the payments to determine the marital portion of the pension payments. This should give you $1,200. 

Nicole's life expectancy, taken from a  give life expectancy table, is 33.56 years, so she should live to be 81.56 years old.

Set your 12C to the beginning of the period and input:

PMT = 1,200 (monthly payment)

n= 198.72 (number of years between age 65 and 81.56 multiplied by 12)

i= .41667 (interest rate divided by 12)

FV= 0

Hit PV. We find that the present value of the monthly payments is $161,759. That is the amount of money needed at age 65 to be able to pay Nicole $1,200 per month for 16.56 years, which is her life expectancy. 

 

Now, calculate the present value as of today fo the final answer:

FV= 161m759

n= 17

i= 5

PMT= 0 (there are no payments until she retires at age 65)

Hit PV. We find that the presnet value of the marital portion is A) $70,575.

 

Thank you guys for all your help. Any additional comments on the above is greatly appreciated. 

 

Best,

Adam

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David_M
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Thanks for providing the text of the problem.  That clarifies some things, and in particular makes it very clear that these are indeed monthly payments instead of annual.  That brings this back into the realm of reality now.

Knowing that the assumed APR is 5%, that changes the PV slightly (only by a few cents) as we now know that the reported interest rate of 0.41667/period was rounded.  It truly should have been 5% annual, which is easily entered as "5 g i" on the 12c.

Here's what the first part now looks like on a 12c:

BEGIN MODE
CLEAR FIN
n: 198.72 (could be entered with 16.56 g n)
i: .4166666667 (could be entered with 5 g i)
PMT: 1200
Solve for PV: -161759.7477

Translated to the 10bII:

BEGIN MODE
C MEM TVM
12 P/YR
198 N (remember that this has to be an integer)
5 I/YR
1200 PMT
Solve for PV: -162245.026929

RCL I ÷ 1200 x 0.72 + 1 = 1.003
1/x x RCL PV = -161759.747686

Notes:
- "I" had to be divided by 1200 in order to convert it from an APR to a decimal monthly effective rate
- I didn't put all the unneeded "=" steps in this version.  The previous ones were there just to allow you to verify each step as you made your way through the calculation.

Now that this has been established, I would humbly suggest that the PV result from the 12c is somewhat misleading.  The presence of the fractional period causes the PV to be calculated in a manner which understates its value within the context of this problem, due to the special meaning that is implied by that type of input on the 12c.  I believe the value calculated on the 10bII using 198.72 for n (-162624.532218) is actually a more realistic figure in this context.  Why?  Well consider the following: what would be the PV of the pension if Nicole's life expectancy made the term exactly 198 or 199 months instead of 198.72?

On both the 12c and the 10bII, the PV of the pension for those given terms is as follows:
198 months: -162245.0269
199 months: -162771.8110

Notice that the 10bII's PV for a term of 198.72 months falls between those figures, and it's closer to 199 than 198.  That seems more reasonable to me than the 12c's PV with the same term, which is even lower than the PV at 198 months.

So I don't know if I'm helping you or not here.  While I've shown a way to make the 10bII give you the same result as the 12c, I actually believe the 10bII's original/simpler result was more meaningful than the adjusted "textbook matching" one that is the same as the 12c's.

 

Edit: I probably should have also included a reference to the section of the 12c User's Guide that refers to the special treatment of an "n" that contains a fractional part.  It starts on page 50 of that guide, in the section titled "Odd-Period Calculations".  The important thing to note about "Odd-period mode" is that it is assumed that the odd period is at the beginning instead of the end, which doesn't align with this particular problem very well.

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LauraC215
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I saw your question and knew right away that you were studying for the CDFA! Me too and I was searching the same issue.  I dealt with this calculation issue on the Module 2 test and it just complicated things and shook my confidence a little during the test. I passed though. I have the final on May 11 and hoped to get this straightened out. Maybe I'll just borrow a 12c.  I'm using 4 decimals, 1 p/yr and end

 

How did you end up dealing with it?  

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adamyoung1983
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I used 5 decimals and BEG. The weird thing was that I switched back and forth between 12 P/YR for the first calculation and then 1 P/YR for the second calculation which got me very close. I’m still confused but was able to get passed the exam. Good luck on the final!
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David_M
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@adamyoung1983wrote:
...The weird thing was that I switched back and forth between 12 P/YR for the first calculation and then 1 P/YR for the second calculation which got me very close.

That's the same thing the study guide did in its proposed solution.

 

Your transcription of the study guide shows that they used 17 for n and 5 for i in the second part of the calculation, which means that they switched from monthly compounding to annual.  There's nothing in the narrative to explain why they did that, however.  Is there a stipulation somewhere in the curriculum that says to assume annual compounding unless otherwise required (such as when monthly payments are involved in the first part)?  Otherwise, it simply seems like an inconsistency.

 

It's one more reason to suggest that the study guide seems to be poorly written for this scenario.

 

Does the publisher offer a specific study guide for the 10bII?  The approach and methods they used for the 12c don't translate well to a calculator that has the features and variable definitions of the 10bII.

 

I'm glad you passed, despite the oddities of this problem. :generic:

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