Solving the TVM equation for the interest rate
02-12-2020, 09:37 PM
Post: #20
 ttw Member Posts: 249 Joined: Jun 2014
RE: Solving the TVM equation for the interest rate
(02-12-2020 05:25 PM)Albert Chan Wrote:  This formula is based on Pade[1,1], I centered 0, of NFV = F + P + ((1+I)^N-1)*(P+M/I)

Solving Pade[1,1] approximated NFV = 0, for 1/I :

$$\Large {1\over I} ≈ {\binom{N}{3}M + \binom{N}{2}P \over \binom{N}{2}M + \binom{N}{1}P} - {\binom{N}{2}M + \binom{N}{1}P \over F + P + M N}$$

Doing the same example, N=11, F=40000, P=0, M=-2564

1/I ≈ (-423060/-141020) - (-141020/11796) = 44102/2949

I ≈ 2949/44102 ≈ 6.687%, which under-estimated true rate (6.780%) by tiny 0.093%

One could use this formula as an initial approximation to Newton's method or something else. A good initial approximation is necessary for all iterations and the your [1,1] Pade looks really good.
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 Messages In This Thread Solving the TVM equation for the interest rate - Dieter - 04-15-2018, 08:39 AM RE: Solving the TVM equation for the interest rate - Gamo - 04-15-2018, 10:46 AM RE: Solving the TVM equation for the interest rate - Dieter - 04-15-2018, 02:55 PM RE: Solving the TVM equation for the interest rate - Ángel Martin - 04-15-2018, 04:37 PM RE: Solving the TVM equation for the interest rate - ttw - 04-16-2018, 05:00 AM RE: Solving the TVM equation for the interest rate - Carsen - 04-15-2018, 05:30 PM RE: Solving the TVM equation for the interest rate - Dieter - 04-15-2018, 06:08 PM RE: Solving the TVM equation for the interest rate - Csaba Tizedes - 02-17-2020, 10:30 AM RE: Solving the TVM equation for the interest rate - Carsen - 04-15-2018, 08:48 PM RE: Solving the TVM equation for the interest rate - Dieter - 04-15-2018, 09:38 PM RE: Solving the TVM equation for the interest rate - Dieter - 04-16-2018, 06:34 PM RE: Solving the TVM equation for the interest rate - Jeff_Kearns - 04-19-2018, 02:56 PM RE: Solving the TVM equation for the interest rate - Dieter - 04-19-2018, 09:45 PM RE: Solving the TVM equation for the interest rate - Erwin - 02-13-2020, 06:00 AM RE: Solving the TVM equation for the interest rate - Albert Chan - 12-05-2020, 04:31 PM RE: Solving the TVM equation for the interest rate - AndiGer - 04-16-2018, 03:44 AM RE: Solving the TVM equation for the interest rate - Gamo - 04-17-2018, 08:59 AM RE: Solving the TVM equation for the interest rate - Dieter - 04-17-2018, 06:50 PM RE: Solving the TVM equation for the interest rate - Gamo - 02-12-2020, 10:50 AM RE: Solving the TVM equation for the interest rate - Albert Chan - 02-12-2020, 12:31 PM RE: Solving the TVM equation for the interest rate - ttw - 02-12-2020, 03:41 PM RE: Solving the TVM equation for the interest rate - Albert Chan - 02-12-2020, 05:25 PM RE: Solving the TVM equation for the interest rate - ttw - 02-12-2020 09:37 PM RE: Solving the TVM equation for the interest rate - Albert Chan - 02-12-2020, 11:40 PM RE: Solving the TVM equation for the interest rate - ttw - 02-12-2020, 09:54 PM RE: Solving the TVM equation for the interest rate - Gamo - 02-13-2020, 06:30 AM RE: Solving the TVM equation for the interest rate - Gamo - 02-13-2020, 10:42 AM

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