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.