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Request TVM formula guidance
12-29-2014, 07:47 PM (This post was last modified: 12-30-2014 07:21 AM by Dieter.)
Post: #16
RE: Request TVM formula guidance
(12-28-2014 06:46 AM)iMatt04bit Wrote:  I am still trying to figure out how that is done - 5 decimal places on the 1st guess!
Sure sounds like rocket science to me. ; )

I can hardly believe it either. Ok, for very large n a limit may exist which can agree with the true root to five or more decimals. But otherwise...

Example – try a standard case: let either FV=0 or PV=0, use a sufficiently large number of periods. Then see how close you get with an estimate of PMT/(FV–PV). ;-)

(12-28-2014 06:46 AM)iMatt04bit Wrote:  I revisited the 2nd root prediction and have a solution that seems to be working.
I can get a first approximation in 4-5 iterations, and then feed that to the Newton solver for an exact value.

Essentially I scan in 10ths of the first root between root-1/10th and 0 + 1/10.
I scan to convergence from top-down, bot-up; and for both pos and neg values simultaneously.

Sounds a bit complicated. ;-)

(12-28-2014 06:46 AM)iMatt04bit Wrote:  I am working on the hypothesis that the absolute value of the 2nd root is less than the absolute value of the primary root (and greater than zero). Does this seem sane?

If two solutions exist, which is the primary root and which is the secondary? In other words: what makes a root primary or secondary? If two roots exist, do they both make sense economically/financially?

(12-28-2014 06:46 AM)iMatt04bit Wrote:  This method solves 2 scenarios (the only ones I have at the moment) which have double roots:

Simply let FV and PV have the same sign (both values positive or negative) and then try different values for PMT. Depending on the latter, either two or no solutions exist.

(12-28-2014 06:46 AM)iMatt04bit Wrote:  N:10 PV:50 PMT:-30 FV:100 with 58.203829688346610, -28.443599888025595
N:10 PV:50 PMT:-30 FV:400 with 53.172213268384720, 14.435871328079967

FTR: the exact 30-digit values are
  –28,443 59988 80255 92557 23584 03219 %
    58,203 82968 83466 11648 87241 82543 %
resp.
    14,435 87132 80799 56974 20470 12989 %
    53,172 21326 83847 24310 46024 13744 %

If your Java version uses standard binary double precision arithmetics you should not trust more than 15 digits. At most. ;-)

Dieter
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Messages In This Thread
Request TVM formula guidance - iMatt04bit - 12-02-2014, 05:33 AM
RE: Request TVM formula guidance - Dieter - 12-03-2014, 09:17 PM
RE: Request TVM formula guidance - Dieter - 12-11-2014, 06:36 PM
RE: Request TVM formula guidance - Dieter - 12-14-2014, 04:24 PM
RE: Request TVM formula guidance - Dieter - 12-17-2014, 01:21 PM
RE: Request TVM formula guidance - Dieter - 12-21-2014, 06:14 PM
RE: Request TVM formula guidance - Dieter - 12-25-2014, 12:42 PM
RE: Request TVM formula guidance - Dieter - 12-29-2014 07:47 PM



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