Fun math algorithms

[Albert Chan]

(10-19-2020 08:51 PM)Albert Chan Wrote:  \(PMT = \large \left(1 + {I\over2} + {(IN)^2 \over 12} \right) ({CAP - RES \over N})
+ ({I\over2}) \normalsize (CAP+RES) \)

If we remove the correction factor, we have the "official car lease formula"

Quote:PMT = (CAP – RES) ÷ TRM + (CAP + RES) x MF, where MF = APR/24 = I/2

Let's try some numbers: CAP = 30000, RES = 15000, 4% APR, 36 months lease.

Official leasing formula:
PMT = 15000/36 + 45000*(4%/24) ≈ 416.67 + 75 = 491.67

Add corrections:
I/2 + (IN)²/12 = (4%/24) + (12%)²/12 = 0.2866667%
Corrections = 416.67 * 0.2866667% ≈ 1.19
PMT = 491.67 + 1.19 = 492.86

Using HP50G Time Value of Money App:
PV = 30000, FV = -15000
N=36, APR=4%, P/YR=12, mode=END → PMT = -492.859775103

Car payment of $492.86, matching our estimate