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172 12: The Equation Solver
File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11
Example Using a Solver Function (USPV): Calculations for a Loan
with an Odd First Period. Suppose an auto purchase is financed with a
$6,000 loan at 13.5% annual interest. There are 36 monthly payments
starting in one month and five days. What is the payment amount?
Use the following formula when the time until the first payment is more
than one month but less than two months. Interest for this odd
(non-integer) period is calculated by multiplying the monthly interest by
the number of days and dividing by 30.
The formula for this loan is:
−
−+
+× + =
1 1
1200
1 0
1200 30
1200
N
ANNI
ANNI DAYS
PV PMT
ANNI
where:
ANNI＝ the annual percentage interest rate.
N＝ the number of payment periods.
DAYS＝ the number of leftover, odd days (an integer from 0 through
30).
PV＝ the amount of the loan.
PMT＝ the monthly payment.
The formula can be rearranged and simplified using USPV, the Solver
function for returning the present value of a uniform series of payments:
5OBL#)1<<;D#$((BA1@FD%(T)"
50:B4F5OL1<<;D#$I<T8("
The keystrokes are:
PV
*(
1
+
ANNI
/
1200
*
DAYS
/
30
)
+
PMT
*
USPV
(
ANNI
/
12:N
)=
0