HP 12C: The C Indicator - Odd Period (Calculating Payment)
There is a C indicator on my HP 12C!
When I bought a HP 12C calculator that was manufactured in Brazil, there was a C indicator on it. It was an odd-period calculation switch that has been a documented feature of the HP 12C.
Odd Period of an Annuity
An odd period of any annuity occurs when the present value (example: loan proceeds) is received before the first period (example: month) occurs.
On the diagram below:
PV: proceeds received
PV0: balance at the start of the first period. This the proceeds plus any interest accrued during the odd period. In general, PV0 > PV.
For example: loan proceeds of $10,000 is received on March 26, 2022 (the PV), with the first payment due at the end of the next month, April 30, 2022. In this case, the loan proceeds were received five days before the "official" first month of the loan which starts on April 1, 2022. The odd period is 5 days, or 5/30 of a month.
In general, all months are considered to be 30 days under a 30/360 calendar system. You can use the actual calendar (365/366-day year) if you wish.
To account for an odd period, add the fractional part of the odd period to the number of payments and store it the [ n ] variable.
There are two ways to calculate odd period interest: simple interest and compound interest.
HP 12 Settings for Odd Period Interest
C indicator: the odd period interest is calculated using compound interest
No C indicator: the odd period interest is calculated using simple interest
The setting is set by pressing [ STO ] [ EEX ].
Casio FC-200V Settings for Odd Period Interest
The Casio FC-200V (and FC-100V (1st and 2nd editions)) has a setting for odd periods. In the Compound Interest app (CPMD), press [ SETUP ] and select dn, then select between CI and SI.
CI: the odd period interest is calculated using compound interest
SI: the odd period interest is calculated using simple interest
This set up is also present in the Simple Interest app (SMPL).
Formulas
If your calculator doesn't have odd period settings, you will need to calculate PV0. Once PV0 is calculated, then proceed to calculate payment, ignoring the odd value for n.
Compound Interest:
PV0 = PV × (1 + I%÷(n×100))^(odd period)
Compound Interest - Monthly Payment, 30/360 Day Calendar:
PV0 = PV × (1 + I%÷(1200))^(days ÷ 30)
Simple Interest:
PV0 = PV × (1 + I% ÷ 100 × odd period)
Compound Interest - Monthly Payment, 30/360 Day Calendar:
PV0 = PV × (1 + I% × days ÷ 36000)
where:
PV = proceeds
PV0 = balance at the beginning of the first period
I% = annual interest rate (not converted to decimal)
odd period = fraction of the year which the odd period represents
days = days of the odd period
These formulas assume end-of-period payments, but also work equally as well for beginning-of-period payments. In practice the difference between the two methods result in a small difference.
Example
Facts:
* Loan proceeds: $17,755.00
* Interest rate: 7%
* Number of monthly payments: 60, payments are due at the end of the month
* Odd period: 15 days, 30/360 calendar
Find the payment.
Compound Interest
HP 12C: press [ STO ] [ EEX ] until the C indicator is on
[ f ] [ x<>y ] (CLEAR FIN)
[ g ] (END)
60.5 [ n ]
7 [ g ] (12÷)
17755 [ PV ]
[ PMT ] returns -352.59
Casio FC-200V: set dn to CI
[ CMPD ]
Set: End
N = 60.5
I% = 7
PV = 17755
P/Y = 12, C/Y = 12
Solve PMT for -352.59
Others:
PV0 = 17755 × (1 + 7 × 15 ÷ 36000)= 17806.71
N = 60
I%/YR = 7
PV = 17806.79
P/Y = 12, C/Y = 12
Solve PMT for -352.59
Simple Interest
HP 12C: press [ STO ] [ EEX ] until the C indicator is off
[ f ] [ x<>y ] (CLEAR FIN)
[ g ] (END)
60.5 [ n ]
7 [ g ] (12÷)
17755 [ PV ]
[ PMT ] returns -352.60
Casio FC-200V: set dn to SI
[ CMPD ]
Set: End
N = 60.5
I% = 7
PV = 17755
P/Y = 12, C/Y = 12
Solve PMT for -352.60
Others:
PV0 = 17755 × (1 + 7÷1200)^(15 ÷ 30) = 17806.79
N = 60
I%/YR = 7
PV = 17806.71
P/Y = 12, C/Y = 12
Solve PMT for -352.60
As you can see, little, if any difference between the two methods.
Are there are any other calculators that can handle odd-period calculations?
I'm hesitant to say yes. How do we know if a finance calculator or the finance mode of a scientific or graphing calculator has handles odd-period calculations? Check the set up or mode settings. If you see an option to set odd periods to simple interest or compound interest, then yes. If not, use the formulas stated above to first calculate PV0 and proceed.
For the record, neither the Texas Instruments BA II Plus nor the Sharp EL-738F do not have not odd-period calculation settings. No graphing calculator or scientific calculator with time value of money modules has this that I know of.
On the Calculated Industries Qualifier Plus IIIFX, use the PV0 amount for the Loan Amount. This calculator can find the prepaid interest, which is based on 30/360 day year, simple interest.
Sources
HP 12C Financial Calculator User's Guide. Hewlett Packard. Edition 5. San Diego, California, United States. 2008. pp. 50-53
FC-200V, FC-100V (2nd Edition/Financial Consultant User's Guide. Casio. Shibuya-ku, Tokyo, Japan. 2021
I will back to the Saturday-Sunday schedule starting on March 4, 2023.
Eddie
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