FPMTSCHED

The FPMTSCHED function calculates a payment schedule (principal plus interest) for paying off a series of fixed-rate installment loans over a specified number of time periods. For each time period, you specify the amount of the loans incurred during that time period and a single interest rate that applies to those loans over their lifetime.

FPMTSCHED calculates the payment for a given time period as the sum of the principal and interest due on each loan that is incurred or outstanding in that period.

Return Value

DECIMAL

The result returned by the FPMTSCHED function is dimensioned by the union of all the dimensions of loans and rates and the dimension used as the time-dimension argument.

Syntax

FPMTSCHED(loans, rates, n, [time-dimension] [STATUS])

Parameters

loans: A numeric expression that contains the initial amounts of the loans. When loans does not have a time dimension, or when loans is dimensioned by multiple time dimensions, the time-dimension argument is required.
rates: A numeric expression that contains the interest rates charged for loans. When rates is a dimensioned variable, it can be dimensioned by any dimension, including a different time dimension. When rates is dimensioned by a time dimension, you specify the interest rate in each time period that applies to the loans incurred in that period. The interest rate for the time period in which a loan is incurred applies throughout the lifetime of that loan. The rates are expressed as decimal values; for example, a 5 percent rate is expressed as.05.
n: A numeric expression that specifies the number of payments required to pay off the loans in the series. The n expression can be dimensioned, but it cannot be dimensioned by the time dimension argument. One payment is made in each time period of the time dimension by which loans is dimensioned or in each time period of the dimension specified in the time-dimension argument. For example, one payment each month is made when loans is dimensioned by month.
time-dimension: The name of the dimension along which the interest payments are calculated. When the time dimension for loans has a type of DAY, WEEK, MONTH, QUARTER, or YEAR, the time-dimension argument is optional, unless loans has multiple time dimensions.
STATUS: Specifies that FPMTSCHED should use the current status list (that is, only the dimension values currently in status in their current status order) when computing the payment schedule. By default FPMTSCHED uses the default status list.

Usage Notes

FPMTSCHED and NA Values

When loans has a value other than NA and the corresponding value of rates is NA, an error occurs.

FPMTSCHED is affected by the NASKIP option. When NASKIP is set to YES (the default), and a loan value is NA for the affected time period, the result returned by FPMTSCHED depends on whether the corresponding interest rate has a value of NA or a value other than NA. Table 7-11, "Effect of NASKIP When Loan or Rate Values are NA for a Time Period" illustrates how NASKIP affects the results when a loan or rate value is NA for a given time period.

As an example, suppose a loan expression and a corresponding interest expression both have NA values for 1997 but both have values other than NA for succeeding years. When the number of payments is 3, FPMTSCHED returns NA for 1997, 1998, and 1999. For 2000, FPMTSCHED returns the payment due for loans incurred in 1998, 1999, and 2000.

FPMTSCHED Ignores the Status of the Time Dimension

The FPMTSCHED calculation begins with the first time dimension value, regardless of how the status of that dimension may be limited. For example, suppose loans is dimensioned by year, and the values of year range from Yr95 to Yr99. The calculation always begins with Yr95, even when you limit the status of year so that it does not include Yr95.

However, when loans is not dimensioned by the time dimension, the FPMTSCHED calculation begins with the first value in the current status of the time dimension. For example, suppose loans is not dimensioned by year, but year is specified as time-dimension. When the status of year is limited to Yr97 to Yr99, the calculation begins with Yr97 instead of Yr95.

Examples

Example 7-100 Calculating a Payment Schedule

The following statements create two variables called loans and rates.

DEFINE loans DECIMAL <year>
DEFINE rates DECIMAL <year>

Suppose you assign the following values to the variables loans and rates.

year             loans         rates
-------------- ---------- ----------
Yr95               100.00       0.05
Yr96               200.00       0.06
Yr97               300.00       0.07
Yr98                 0.00       0.00
Yr99                 0.00       0.00

For each year, loans contains the initial value of the fixed-rate loan incurred during that year. For each year, the value of rates is the interest rate that is charged for any loans incurred in that year; for those loans, this same rate is charged each year until the loans are paid off.

The following statement specifies that each loan is to be paid off in three payments, calculates the schedule for paying off the principal and interest on the loans,

REPORT W 20 HEADING 'Payment' FPMTSCHED(loans, rates, 3, year)

and produces the following report.

YEAR                        Payment
-------------- --------------------
Yr95                          36.72
Yr96                         111.54
Yr97                         225.86
Yr98                         189.14
Yr99                         114.32

The payment for 1995 is the principal due on the loan of $100 incurred in 1995, plus interest on the loan at 5 percent. The payment due in 1996 is the sum of the second payment on the loan incurred in 1995 (principal plus 5 percent interest), plus the first payment on the loan of $200 incurred in 1996 (principal plus 6 percent interest). The 1997 payment is the sum of the third and final payment on the loan incurred in 1995, the second of the three payments on the 1996 loan, and the first payment on the loan of $300 incurred in 1997 (principal plus 7 percent interest). Since the 1995 loan is paid off in 1997, the payment for 1998 covers the principal and interest for the 1996 and 1997 loans. The payment for 1999 is the final payment of principal and interest for the 1997 loan.

Example 7-101 Determining Monthly Payments

The following statement determines what the monthly payments would be on a $125,000 loan with an 8.75 percent annual interest rate,

SHOW FPMTSCHED(125000, .0875/12, 360, month)

and produces the following output.

983.38