The TVM menu deals with financial transactions where each payment period is the same length. However, sometimes the first payment period is not the same length as the remaining periods. The date the interest begins accruing to the date of the first payment, when not equal to the regular payment period, is sometimes referred to as an odd first period.
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HP 17bII, 17bII+, and 19bII Calculators  OddPeriod Calculations
Entering and using the odd equation
The following procedure calculates N, I%, PV, PMT, of FV for transactions involving an odd first period. Simple interest accrues during the odd period and is added to the loan at the beginning of the first full period. The equation is valid for 0 to 59 days, and monthly payments with a 30day month is assumed.

Enter the ODD equation into the solver:ODD:PV x (I% / 100 x FP(DAYS/30)+1=IF(DAYS<30:(1+I% / 100) x PMT: PMT) x USPV (I% : N) – FV x SPPV (I%:N)

Display the ODD equation’s menu

Store or calculate the following variables. Remember to use the cashflow sign convention (money paid out is negative, money received is positive).

Loan amount in PVPeriodic Interest rate as a percent in I%Actual number of days until the first payment is made in DAYSPeriodic payment amount in PMTTotal number of payments in NBalloon payment amount in FV
Example of odd period calculation
A 36month loan for $4,500 has an interest rate of 15 percent. If the first payment is made in 46 days, what is the monthly payment?
Display the odd equation’s menu, then follow these steps:
Keys

Display

Description

36 {N}

N=36.00

Stores known values.

4500 {PV}

PV=4,500.00
 
15/12 {I%}

I% = 1.25
 
46 {DAYS}

DAYS = 46.00
 
0 {FV}

FV = 0.00
 
{PMT}

PMT = 157.03

Calculates monthly payment amount.

Example of odd period calculation with balloon
A $10,000 loan has 24 monthly payments of $400, plus a balloon payment of $3,000 at the end of month 24. If the payments begin in eight days, what is the interest rate being charged?
Display the odd equation’s menu, then follow these steps:
Keys

Display

Description

10000 {PV}

PV=10,000.00

Stores known values

24 {N}

N=24.00
 
400[+/] {PMT}

PMT=400.00
 
3000[+/] {FV}

FV=3,000.00
 
8 {DAYS}

DAYS=8.00
 
{I%}

I%=1.64

Calculates monthly interest rate.

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