CALC 1 Home Documentation Home Contact

# Payment for Odd First Period Calculator

Calculates a loan with an odd (partial) first payment period. Formula: (-IF(NOT(GESTEP(Dys, 30)), (1+IPct/100)*Pymt,Pymt )*(1-(1+IPct/100)^(-N))/(IPct/100)-FVal*((1+IPct/100)^-N))/(IPct/100*(Dys/30-TRUNC(Dys/30,0)) +1)

PV (PVal): The present value of the loan.

i% (IPct): The periodic interest rate as a percent.

DYS: The actual number of days until the first payment is made.

PMT (Pymt): The periodic payment.

N: The total number of payment periods.

FV (FVal): The balloon payment. Occurs at the end of the last (Nth) period and is in addition to any periodic payment.

Note that this formula actually calculates the present value (PVal). So to solve for the payment, it is best to enter an initial guess.

## Example 1

A 36 month loan of 4,500 has an annual rate of 15% (15/12 = 1.25) and a balloon payment of 100. If the first payment is made in 46 days, what is the payment?

Value Keystrokes Display Description
4500 PV 4,500.0000 Stores the PVal value.
1.25 i% 1.2500 Stores the IPct value.
46 DYS 46.0000 Stores the DYS value.
-1 PMT -1.0000 Stores the Pymt initial guess value.
36 N 36.0000 Stores the N value.
-100 FV -100.0000 Stores the FVal value.
PMT 154.8174 Calculates Pymt.

## Example 2

If there is no balloon payment, what is the periodic payment?

These keystrokes assume the values from example 1.

Value Keystrokes Display Description
0 FV 0.0000 Stores the FVal value.
PMT -157.0339 Calculates Pymt.

Reference:

These examples agree with the HP-17BII "additional Examples".

The results using this formula calculator agree with the payodd() function example given at Payment of loan or annuity with odd first period, MathWorks.