Fun math algorithms

[Albert Chan]

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