Looking for TVM formulas
04-05-2014, 09:58 PM (This post was last modified: 04-05-2014 10:22 PM by Dieter.)
Post: #24
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Looking for TVM formulas
(04-04-2014 10:12 PM)Dave Britten Wrote:  3. Five "solve" routines - Three of these are direct solutions (PV, PMT, FV), and the other two prepare...
4. ...The numeric solver - A straight port of the HP 20S solver, with a couple changes specific to this progra. It chokes on overflows trying to solve for n or i% in the Susan example,

Hm, why do you think that there is no direct solution for n and an iterative approach is required?

Consider the basic TVM formula you already posted:

PV * (1 + i)n + PMT * ((1 + i)n – 1)) * ((1 / i) + B) + FV = 0

Then
(1 + i)n – 1 = –(PV + FV) / (PMT * (1 / i + B) + PV)

And thus, using ln1+x for best accuracy:

n = ln1+x(–(PV + FV) / (PMT * (1 / i + B) + PV)) / ln1+x(i)

Or a bit more formal:

$$\large n = ln (1 - \frac{PV + FV}{PV + PMT (\frac{1}{i} + B)}) : ln (1 + i)$$

Try the Susan example:

(1+i)n – 1 = (–(0 + -333783,35)) / ( 0,01 * (1/3,567351598 E-9 + 0) + 0) = 333783,35 / 2803200 = 0,1190722567

ln1+x(0,1190722567) / ln1+x(3,567351598 E-9) = 31536000

Dieter
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 Messages In This Thread Looking for TVM formulas - Dave Britten - 03-31-2014, 11:21 PM RE: Looking for TVM formulas - Thomas Klemm - 04-01-2014, 12:17 AM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 12:43 AM RE: Looking for TVM formulas - Thomas Klemm - 04-01-2014, 04:25 AM RE: Looking for TVM formulas - Jeff_Kearns - 04-01-2014, 10:40 AM RE: Looking for TVM formulas - Manolo Sobrino - 04-01-2014, 09:36 AM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 01:16 PM RE: Looking for TVM formulas - Jeff_Kearns - 04-01-2014, 07:37 PM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 08:01 PM RE: Looking for TVM formulas - Dieter - 04-02-2014, 12:21 PM RE: Looking for TVM formulas - Dave Britten - 04-02-2014, 02:15 PM RE: Looking for TVM formulas - Thomas Klemm - 04-02-2014, 05:18 PM RE: Looking for TVM formulas - Dieter - 04-02-2014, 07:23 PM RE: Looking for TVM formulas - Dieter - 04-06-2014, 07:46 PM RE: Looking for TVM formulas - Dieter - 04-09-2014, 01:36 PM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 06:01 PM RE: Looking for TVM formulas - Manolo Sobrino - 04-02-2014, 04:55 PM RE: Looking for TVM formulas - Dieter - 04-02-2014, 07:40 PM RE: Looking for TVM formulas - Manolo Sobrino - 04-03-2014, 01:10 AM RE: Looking for TVM formulas - Dieter - 04-03-2014, 01:22 PM RE: Looking for TVM formulas - Manolo Sobrino - 04-04-2014, 07:49 AM RE: Looking for TVM formulas - Dave Britten - 04-04-2014, 02:07 PM RE: Looking for TVM formulas - Thomas Klemm - 04-04-2014, 05:23 PM RE: Looking for TVM formulas - Jeff_Kearns - 04-04-2014, 09:44 PM RE: Looking for TVM formulas - Dave Britten - 04-04-2014, 10:12 PM RE: Looking for TVM formulas - Dieter - 04-05-2014 09:58 PM RE: Looking for TVM formulas - Dave Britten - 04-05-2014, 11:38 PM

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