(12C) Mortgage Loan Interest Rate

06152021, 07:45 AM
(This post was last modified: 06152021 07:58 AM by Gamo.)
Post: #1




(12C) Mortgage Loan Interest Rate
This program was modify and adapted to work for the HP12C from
HP33E Applications Book on Page 37 As state in this book program will calculate the interest rate on a loan with equal periodic payments. The user must specify the number of period, the present value or initial loan amount, and the payment amount. The program performs an iterative solution for [i] using Newton's method. Usually this type of problem can be solve easily with the HP12C but I found that this program run faster than the Original HP12C when solve for "Interest Rate" So this program is use to try out the computation speed between the buildin TVM functions and the custom program.  Example Problem: n = 36 PV = 3600 PMT = 360 Interest Rate = ? [f] 2 36 [n] 3600 [PV] 360 [CHS] [PMT] [i] ...... about 17 second display 9.64 To use program: same data as previous problem press [R/S]....... about 12 second display 9.64  Program: Code:
Remark: This program speed don't make noticeable different on the HP12C+ I think the reason that this program run faster might be how this program use the initial guess (The guess migh be very close to the solution than the HP12C TVM algorithm) Gamo 6/2021 

06152021, 01:13 PM
Post: #2




RE: (12C) Mortgage Loan Interest Rate
(06152021 07:45 AM)Gamo Wrote: [f] 2 It seems HP12C use whatever was stored in [i] as guess. If we provide same guess of program for HP12C TVM: (PMT/PV)  (PV/PMT)/N² ≈ 1/10  10/36² ≈ 9.23% 9.23 [i] [i] ... finished in 10 second Solve again, with true rate as guess [i] [i] ... finished in 4 second With 5% guess, and interrrupt rate search, we get this: 5 [i] [i] [On] [On] → 8.99 [i] [i] [On] [On] → 9.62 [i] [i] [On] [On] → 9.64 

06162021, 06:00 AM
Post: #3




RE: (12C) Mortgage Loan Interest Rate
According to this book state that
The initial guess for [i] is given by i₀ = PMT ÷ PV  (1 ÷ n²) PV ÷ PMT Gamo 

06162021, 03:28 PM
Post: #4




RE: (12C) Mortgage Loan Interest Rate
Timing suggested solving for i is using IRR routine.
Clear Reg 3600 CF0 ; PV 360 CHS CFj ; PMT 36 Nj ; N IRR ; 9.635443543 (17 sec) 9.23 [i] RCL [g] [R/S] ; guess = (PMT/PV)  (PV/PMT)/N^2 (10 sec) [i] RCL [g] [R/S] ; guess = true rate (4 sec) 

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