Solving the TVM equation for the interest rate

02122020, 09:54 PM
Post: #21




RE: Solving the TVM equation for the interest rate
I'd like to add that getting these interest rates is more important than most people realize. Of course, most math is more important i everyday life than most people understand for that matter.
When comparing two investments or two mortgages or something similar, one should always choose the investment with the best rate or mortgage with the least (if the payments are affordable.) It' isn't (as the radio and TV pseudo financial pseudo advisors sometime say) that one compares the "total of interest payments" or worrying about monthly payments for a purchase no longer owned (or even paying a ballplayer who's been traded.) It's only the interest rate (AKA "rate of return.") A short term mortgage mortgage (15 vs 30) years may have bigger payments but lower interest rates; if one can afford it, the lower rate always give bigger bang for the buck. The same with investments; get the best rate of return. A lower rate on car payments may make longer terms favorable; one may be paying for car (or ball player or house) already traded or sold to achieve a low effective interest rate. Likewise, higher interest means faster retirement fund growth. 

02122020, 11:40 PM
Post: #22




RE: Solving the TVM equation for the interest rate
(02122020 05:25 PM)Albert Chan Wrote: This formula is based on Pade[1,1], I centered 0, of NFV = F + P + ((1+I)^N1)*(P+M/I) We can reuse the formula, getting a closer estimate. With above I=6.687%, calculated F = 39804.11, error = 40000  39804.11 = 195.89 Tried the formula again, with F = 40000 + 195.89, to compensate this error I ≈ 1/(3  (141020/(11796 + 195.89))) ≈ 6.775% Again, using this new I, calculated F = 39989.83, error = 40000  39989.83 = 10.17 Interpolate for 0 error, I = 6.775%  (6.687%  6.775%) * 10.17/(195.89  10.17) = 6.7798% 

02132020, 06:00 AM
Post: #23




RE: Solving the TVM equation for the interest rate
(04152018 08:48 PM)Carsen Wrote: Problem #1: n=32 PV=6,000 FV=10,000 PMT=0 i=??? Hello, cause I was curious I tried the above examples with the finance pac from the HP71b with the following solutions: Problem #1: i= 1.609139492% same as the 12c Problem #2: i= 0.169257426% Problem #3: i= 0.562601665% Problem #4: i= 0.458330232% So it looks like, that the HP71b routine for small interest rates use a different method compared to the other calculators. But no idea what calculation method the HP71b use, there are no hints in the user manual. regards Erwin 

02132020, 06:30 AM
Post: #24




RE: Solving the TVM equation for the interest rate
Albert Chan
Thanks for the comment, I found that in the HP55 Mathematics Programs On the Direct Reduction Loan Interest Rate the program used the Harmonic Mean approach for the Suggested Guess solution but the book doesn't show the formula on this I'll find out about this approach later. Thanks Gamo 

02132020, 10:42 AM
(This post was last modified: 02132020 10:46 AM by Gamo.)
Post: #25




RE: Solving the TVM equation for the interest rate
From HP55 Mathematics Programs
The Suggested Guess for 1. Direct Reduction Loan Interest Rate with known [n, PV and PMT] 2. Sinking Fund Interest Rate with known [n, FV and PMT] To find the guess the HP55 programs book used these formulas. 1. Direct Reduction Loan Interest Rate [1 / (PV / PMT)]  [(1 / n^2) x (PV / PMT)] 2. Sinking Fund Interest Rate [((FV/PMT)  n) x 2] ÷ [(n  1)^2 + (FV/PMT)] Gamo 2/2020 

02172020, 10:30 AM
Post: #26




RE: Solving the TVM equation for the interest rate
(04152018 05:30 PM)Carsen Wrote:(04152018 08:39 AM)Dieter Wrote: So the result seems to depend on previous input ?!I believe you are right Dieter. Try this on your HP12C emulator. IMHO there is a test for result=0 AND if the test is false the algorithm checks the abs(ch% of result)<=eps%. It seems a more possible explanation. Csaba 

12052020, 04:31 PM
(This post was last modified: 06162021 02:20 PM by Albert Chan.)
Post: #27




RE: Solving the TVM equation for the interest rate
(04152018 08:48 PM)Carsen Wrote: Problem #1: n=32 PV=6,000 FV=10,000 PMT=0 i=??? I made function guess_i(n, pv, pmt, fv), fitting TVM of i as quadratics lua> guess_i(32,6000,0,10000) * 100 1.609603176046163 lua> guess_i(36,13000,372.53,0) * 100 0.16925501753153394 lua> guess_i(36,5750,176.89,0) * 100 0.5625467055347055 lua> guess_i(360,75000,425.84,0) * 100 0.4601135680666762 Car leasing example, taken from Fun math algorithms FV is negative, because we are returning the car, at the end of the lease. lua> guess_i(36, 30000, 550, 15000) * 1200 6.9657545218584485 Using HP12C, actual APR = 6.966087383% Update: numbers adjusted with updated guess_i() 

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