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Solving the TVM equation for the interest rate
04-19-2018, 02:56 PM (This post was last modified: 04-19-2018 03:29 PM by Jeff_Kearns.)
Post: #14
RE: Solving the TVM equation for the interest rate
(04-15-2018 08:48 PM)Carsen Wrote:  Problem #1: n=32 PV=-6,000 FV=10,000 PMT=0 i=???
Answers: 12C=1.609139492% 15C=1.609139501% Prime=1.60913949196%

Problem #2: n=36 PV=13,000 PMT=-372.53 FV=0 i=???
Answers: 12C=0.1692576094% 15C=0.1692569782% Prime=0.169257604168%

Problem #3: n=36 PV=5,750 PMT=-176.89 FV=0 i=???
Answers: 12C=0.56266017270% 15C=0.5626013555% Prime=0.562601726101%

Problem #4: n=360 PV=75,000 PMT=-425.84 FV-0 i=???
Answers: 12C=0.458302324% 15C=0.4583302039% Prime=0.458330232637%

When I try using a standard initial estimate of 0.001% for the interest rate for each of the above examples with the HP-15C TVM program (40 lines in length), I get the following results. I then compared them to the HP-19BII (reference result), and the HP-29C (71 line adaptation using Stefan Vorkoetter's Equation Solver for the HP-19C):

Problem #1: n=32 PV=-6,000 FV=10,000 PMT=0 i=???
Answers: 15C=1.609139493%; 19BII=1.60913949223%; 29C=1.609139493

Problem #2: n=36 PV=13,000 PMT=-372.53 FV=0 i=???
Answers: 15C=0.169257612%; 19BII=0.16925760942%; 29C=0.169257597

Problem #3: n=36 PV=5,750 PMT=-176.89 FV=0 i=???
Answers: 15C=0.562601729%; 19BII=0.56260172701%; 29C=0.562601732

Problem #4: n=360 PV=75,000 PMT=-425.84 FV-0 i=???
Answers: 15C=0.458330232%; 19BII=0.45833023240%; 29C=0.458330233

I actually use the HP-15C LE instead of the 15C since it is much, much faster ;-). The 15C program is located here. The 29C program can be found here. For the fourth example, I initially got an error on the 29C, but then I simply changed the estimate range from [0.001% to 0.2%] and got a satisfactory answer.

The 15C program is an adaptation of the Pioneer's (42S/35S/33S/32Sii/32S) Accurate TVM routine, modified using Karl Schneider's technique for invoking SOLVE with the routine written as a MISO (multiple-input, single-output) function, using indirect addressing. As I recall, Nick stated back in August 2016 that the program fails in special cases where I = 0, but then why use a TVM program at all when there is no interest rate? TVM implies some interest, after all. I have found this program easy to use with mnemonics to remember the storage registers, and quite useful for my purposes. The mnemonics are kind of silly (No Interest Before Payment of Funds; where N=STO 1, I=STO 2, B or PV=STO 3, P=STO 4, and F=STO 5) but they are easy to remember. The 29C program also works on the 11C.

I may be missing the point of this thread, and apologize if that is the case. If it is, can someone please explain the issue.

Jeff
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RE: Solving the TVM equation for the interest rate - Jeff_Kearns - 04-19-2018 02:56 PM



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