HP -18C Owner's Manual page 148

Example: Calculations for a loan with an odd first period. An
auto purchase is financed with a $6,000 loan at 13.5% annual inter-
est. There are 36 monthly payments to be made starting in one month
and five days. What is the payment amount?
The following formula is used when the time period until the first
payment is more than one month but less than two months. Interest
for the odd period is calculated by multiplying the monthly interest
by the number of days and dividing by 30.)
The formula for this loan situation is:
PV
(1
+
ANNI x DAYS)
+
PMT
(1
1200 30
_ (1
+
ANNI)-N)
1200
=
0
ANNI
1200
where:
ANNI
=
The annual percentage interest rate.
N
=
the number of payments.
DAYS
=
the number of odd days (an integer in the range 0 through
30).
PV
=
the amount of the loan.
PMT
=
the monthly payment.
The formula can be rearranged and typed into the solver as:
PVXC1+ANNI+1200xDAYS+30)
+PMTxUSPVCANNI+12:N)=0
where USPV is the solver function for returning the present value of
a uniform series of payments.
146 9: The Formula Solver