TVM calculations (again)



#9

Hi,

a few weeks ago I complained about some miscalculations concerning TVM and a HP-18c et al. The method usually used to calculate the FV for payments that occur at a different period than the interest compoundings is to convert the interest prior to the TVM calculation. Thats not ok if payments are made more often than interest compoundings. I found by iterating over payments and a subsequent iteration over compoundings that

FV=PV*q^j+a*(q^j-1)/(q-1)

where

a=PMT*(n+p%*(n+1)/2)

if payments are made at the beginning of the payment period and

a=PMT*(n+p%*(n-1)/2)

if payments are made at the end of the payment period.

(q=(1+p%),j=interest compounding periods,n=payment periods per comp.period)

Note that the payment convention is strictly german i.e., the PV and PMT are signed (the germans are thinking in 'savings accounts' instead of loans;).

Well, I thought I had something to publish here as noone I asked could tell me anything else than to use the faulty method described first. Too bad, I recently found an older source which mentions equations similar to mine:(. Anyway, I did the same for the case where payments occur less often than interest compoundings and found for begin and end of period payments

FV=PV*q^(n*j)+PMT*q^j*(q^(j*n)-1)/(q^j-1)

and

FV=PV*q^(n*j)+PMT*q^j*(q^(j*(n-1))-1)/(q^j-1)

(n=payment periods,j=comp.periods per payment period)

respectivly. This is--probably by accident>:)--exactly what ICONV+TVM gives (You have to check this by hand as Maple refuses to validate it correctly:). It's just in a more compact shape and easier to use.

bye,

Thomas (Who is still seeking for (i) a job anywhere in the western world and (ii) a cheap 28C to accompany his 18C:)


#10

Thanks for your posting.

Do you have any comparison of the results and accuracy of your method against HP calculators?

I have a 12C, 10B, 10BII, 14B, 17BII, 38C, and a finance pac for the 71B. Also the HP finance program for the 11C.

If you would like any results from these let me know.


#11

Gordon,

I have to admit that the 18C is my only financial calculator. I've heard that the 11C and 17BII uses the same TVM equation as the 18C. Anyone else could most probably answer that better than me.

About the FV problem where payments are made more often than interest is compounded, the commonly propagated solution to convert the interest to an effective or nominal interest from an 'equivalent interest' and then to use the TVM equation is actually not just inaccurate but completly false. Therefore it makes no sense to compare results.

Some of your calculators offer a convenient solver (like the 18C) and I would recommend to just enter the equations I gave in case you need them.

Thomas

#12

Hi Thomas - good luck finding the job and the 28C :)

I finally found a savings example from HP where payment frequency > compounding frequency. It is Example 2 on page 48 of the HP-12C solutions handbook. They get $11.49 for the weekly payment in advance to fund $6000 over 8 years at 5.5% compounded quarterly. This assumes the compound interest operates as a continuous geometric process. If simple interest (an arithmetic process) applies over each quarter then I obtain the same PMT - rounded to the penny - 11.4942 as against 11.4944 for the compound assumption. Pretty close in this case.

On page 46 they state "Payments deposited for a partial compounding period will [usually?]accrue simple interest for the remainder of the compounding period. This is often the case, but may not be true for all institutions."

Cheers,
Tony


#13

Hi Tony,

the example was probably choosen to give a result thats close to be correct:).

I personally think HP should do a better job to make their financial calculators of more general use. But ok, I'm not an expert and hundreds of thousands of users are apparently satisfied with what is offered.

Thomas


#14

Thomas, yes undoubtedly why they chose that example :)

I agree with you 100% - in none of the HP manuals I have and even Grapevine books
is there an example of the simple interest FV of a series of payments, and how to
use that.

I have seen it in one old book though - "Modern Financial Computation" published
in 1983, by Tony Hutchins<G>. There is a chapter called "Simple Interest During
Compounding Periods", from pages 115-135, together with 5 loan examples and 6
savings examples. This 270pp book (wirebound) is still available from the author
but he has to charge about 50USD for it to cover cost and airmail postage from
New Zealand. So, he doesn't sell many copies - keeps life simple<G>.


#15

Hi Tony,

Seems to be an excellent book;), I would buy it if I could effort it:).

Thomas


#16

Thomas, I did have a copy with me in Munich in May last year - would have been
happy to trade it for a beer :)

Today I was surprised (and delighted) to receive three inquiries about it so I
scanned the introduction and contents and put them at:

http://homepages.paradise.net.nz/th/mfc.htm

Cheers,
Tony


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