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Fun math algorithms
10-17-2020, 11:27 AM (This post was last modified: 10-17-2020 01:54 PM by Albert Chan.)
Post: #9
RE: Fun math algorithms
Hi, EdS2

I was cutting off taylor series of C-1, eliminated O(I³) terms, then eliminated I only terms.

C-1 = I*(N+1)/2 + I²*(N²-1)/12 + ... ≈ (IN)/2 + (IN)²/12 = IN*(6+IN)/12

Keeping I only terms make better estimate, but more computations.
Update: to reduce computations, we ignore I² only term.

C-1 ≈ I*(N+1)/2 + I²*(N²-1)/12 = IN*(6+IN)/12 + I*(6-I)/12 ≈ IN*(6+IN)/12 + I/2

Redo example, PV=33631, I=3.6%/12=0.3% , N=5*12=60

C-1 ≈ IN*(6+IN)/12 + I/2 = 9.27% + 0.15% = 9.42%

Fixed 2 mode:
33631 Enter 60 /    → 560.52 (monthly payment, if no interest)
9.42 %              →  52.80 (monthly finance charge, estimated)
+                   → 613.32 (monthly payment, estimated)

Car payment over-estimated only 1 penny Smile
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Messages In This Thread
Fun math algorithms - Han - 09-05-2020, 10:31 PM
RE: Fun math algorithms - telemachos - 09-06-2020, 12:30 AM
RE: Fun math algorithms - Albert Chan - 09-06-2020, 12:46 AM
RE: Fun math algorithms - Han - 09-06-2020, 03:54 AM
RE: Fun math algorithms - Albert Chan - 09-08-2020, 09:59 PM
RE: Fun math algorithms - David Hayden - 09-10-2020, 03:59 PM
RE: Fun math algorithms - Albert Chan - 10-16-2020, 04:02 PM
RE: Fun math algorithms - EdS2 - 10-17-2020, 08:51 AM
RE: Fun math algorithms - Albert Chan - 10-17-2020 11:27 AM
RE: Fun math algorithms - Albert Chan - 10-17-2020, 12:32 PM
RE: Fun math algorithms - EdS2 - 10-19-2020, 07:59 AM
RE: Fun math algorithms - Albert Chan - 10-19-2020, 08:51 PM
RE: Fun math algorithms - Albert Chan - 10-19-2020, 09:33 PM
RE: Fun math algorithms - Albert Chan - 10-19-2020, 11:05 PM



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