HP Forum Archive 13

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TVM accuracy revisited Message #1 Posted by Tommi on 3 Sept 2003, 3:13 a.m. Heylo! Was looking for a good TVM program for my HP41CX and found the improved FI (FIN) program in PPC Journal 1983 Jan/Feb, p.22f. Great program btw :) In another thread, the first accuracy problem presented in the PPC article was discussed. What is really the most "correct" answer here??? According to the PPC article, the HP12C in those days returned FV=-1,244,458.491 (in the previous thread, the incorrect FV=-1,237,786.903 is mentioned for 12C/P, but the payment period is BEGIN, not END). The PPC article goes on to calculate the trouble-some interest rate using the super accurate function (((1+i)^n)-1)/i, where n can be fractional (available on e.g. HP-37E in those days, but not 12C or HP41). This will give FV=-1,244,458.519. (The above function do exist in 12C, but only works with INT(n). What about 12CP?) The improved FI (FIN) program for HP41 presented in the article, will give FV=-1,244,458.520, using the accurate E^X-1 and LN1+X functions available on the HP41. Interestingly, my HP49G emulator (ROM version 1.18) returns FV=-1,244,458.523. Do we have 10 significant digits here somewhere for FV? HP12C : -1,244,458.491 HP41C : -1,244,458.520 HP37E : -1,244,458.519 (returns same as 12C in normal use) HP49G : -1,244,458.523

Re: TVM accuracy revisited Message #2 Posted by Victor Koechli on 3 Sept 2003, 7:29 a.m., in response to message #1 by Tommi And which would be the correct answer?

Re: TVM accuracy revisited Message #3 Posted by Rodger Rosenbaum on 3 Sept 2003, 8:09 p.m., in response to message #1 by Tommi Tommi says: "Do we have 10 significant digits here somewhere for FV? HP12C : -1,244,458.491 HP41C : -1,244,458.520 HP37E : -1,244,458.519 (returns same as 12C in normal use) HP49G : -1,244,458.523" The interest rate in this problem is (lots of digits): i=.538 993 302 623 106 141 922 The FV is (lots of digits): FV=-1,244,458.519 105 488 899 859 678 Interestingly, if one computes the interest rate with the following sequence on the HP17B II (or some similarly Saturn based financial calc) (begin mode) 1 N 15 I%YR 100 PV FV 26 N I%YR one gets i=.538 993 302 622 But if one uses the LNP1 and EXPM1 functions on the HP48 and evaluates EXPM1(LN(1.15)/26) one gets: .538 993 302 623 I'm sure one of the things the later financial calcs, especially the Saturn based ones, did to improve accuracy is to use an internal LNP1 and EXPM1 where appropriate. So why the discrepancy in the LSD? If this problem is solved with the HP48's TVM solver, and the interest rate is calculated with the keystroke sequence: (begin mode) 1 N 15 I%YR 100 PV FV 26 N I%YR the result is -1,244,458.51909 But if the interest rate is calculated as EXPM1(LN(1.15)/26), and this is stored in I%YR, and the FV is solved for, the result is: -1,244,458.5191, which is more nearly correct . I hadn't before seen a result where the internal result of a Saturn based financial calc is less accurate than what I can calculate myself with the LNP1 and EXPM1 functions.

Re: TVM accuracy revisited Message #4 Posted by Rodger Rosenbaum on 3 Sept 2003, 8:19 p.m., in response to message #3 by Rodger Rosenbaum In the interest of clarity, in my previous posting, where I said: If this problem is solved with the HP48's TVM solver, and the interest rate is calculated with the keystroke sequence: (begin mode) 1 N 15 I%YR 100 PV FV 26 N I%YR the result is -1,244,458.51909 Replace with: If this problem is solved with the HP48's TVM solver, and the interest rate is calculated with the keystroke sequence: (begin mode) 1 P/YR 1 N 15 I%YR 100 PV FV 26 N I%YR Then type 1040 N 0 PV 25 PMT FV the result is -1,244,458.51909

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