HP 17BII+ and Numworks: Payment of a Loan with an Unusual First Period
The First Payment Is Not Due in a Month
In finance, the first payment of a loan is not due at the end of a month from signing. This happens when all payments are due at a certain date, such as the 30th/31st or 1st of each month, regardless of when the loan papers are signed. Loans of this type are referred to odd period loans or partial period loans. Every payment after the first follows the conventional month time line.
HP 17BII+ Formula: Partial Period Loan
The following HP 17BII+ formula deals with calculating odd period loans. This solver formula is directly from the HP 17BII+ Financial Calculator User's Guide, pg. 196 (see source):
ODD: PV×(I%÷100×FP(DAYS÷30)+1)=-IF(DAYS<30:(1+I%÷100)×PMT:PMT)×UPSV(I%:N)-FV×SPPV(I%:N)
In the solver, the percent sign is a character used in variables, not a function. PV, FV, PMT, I%, N are all valid variables in the HP 17BII+ solver. The variables:
N: number of payments
DAYS: number of days in the first period, from 0 to 59.
I%: the periodic interest rate. For monthly payments, divide the annual interest rate by 12.
PV: the loan amount
FV: the balloon amount
PMT: payment
This formula follows the cash flow convention: negative amounts for cash outflows, positive amounts for cash inflows.
Numworks Script: Partial Period Loan
oddperiod.py
My Numworks script: https://my.numworks.com/python/ews31415/oddperiod
# 2021-11-14 EWS
# odd period
from math import *
print("Loan with partial period")
print("0 - 59 days")
print("Monthly Payments")
n=float(input("N: n? "))
rate=float(input("I/YR: rate? "))
pv=float(input("PV: loan amt? "))
fv=float(input("FV: balooon pmt? "))
days=float(input("DAYS: odd period? "))
r=rate/1200
if days<30:
j=1+r
else:
j=1
f=days/30-int(days/30)
w=r*f+1
# uspv
u=(1-(1+r)**(-n))/r
# sppv
s=(1+r)**(-n)
pmt=(pv*w+fv*s)/(j*u)
# rounding
pmt=-int(pmt*100+.5)/100
# result
print("Payment: "+str(pmt))
Note: the cash flow convention is followed
Examples
Loan 1:
Inputs:
N = 60
DAYS = 10
PV = $58,425.10
I%/YR = 4.48% (annual rate), for the HP 17BII+, divide this by 12
FV = $0.00 (no balloon payment)
Result: PMT: -1,085.99
Loan 2:
Inputs:
N = 240
DAYS = 40
PV = $16,956.00
I%/YR = 7.02% (annual rate), for the HP 17BII+, divide this by 12
FV = $500.00 (enter -500.00 for HP 17BII+)
Result: PMT: -130.96
Source
HP 17BII+ Financial Calculator User's Guide. Ed. 2. Hewlett Packard. San Diego, CA 2004
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