payment¶

Evaluates the periodic payment for an investment.

Synopsis¶

payment (rate, nPeriods, presentValue, futureValue, when)

Required Arguments¶

float rate (Input): Interest rate.
Int nPeriods (Input): Total number of periods.
float presentValue (Input): The current value of a stream of future payments, after discounting the payments using some interest rate.
float futureValue (Input): The value, at some time in the future, of a current amount and a stream of payments.
int when (Input): Time in each period when the payment is made, either AT_END_OF_PERIOD or AT_BEGINNING_OF_PERIOD. For a more detailed discussion on when see the Usage Notes section of this chapter.

Return Value¶

The periodic payment for an investment. If no result can be computed, NaN is returned.

Description¶

Function payment computes the periodic payment for an investment.

It can be found by solving the following:

If rate =0

\[\textit{presentValue} + (\textit{payment})(\textit{nPeriods}) + \textit{futureValue} = 0\]

If rate ≠ 0

\[\begin{split}\begin{array}{l} \mathit{presentValue}(1+\mathit{rate})^{\mathit{nPeriods}} + \\ \mathit{payment}[1 + \mathit{rate}(\mathit{when})] \frac{(1+\mathit{rate})^{\mathit{nPeriods}}-1}{\mathit{rate}} + \mathit{futureValue} = 0 \end{array}\end{split}\]

Example¶

In this example, payment computes the periodic payment of a 25-year $100,000 loan with an annual interest rate of 8%. The payment is made at the end of each period.

from __future__ import print_function
from numpy import *
from pyimsl.math.payment import payment, AT_END_OF_PERIOD

rate = 0.08
n_periods = 25
present_value = 100000.00
future_value = 0.0
when = AT_END_OF_PERIOD

payment_amt = payment(rate, n_periods, present_value,
                      future_value, when)
print("The payment due each year on the $100,000 loan is $%.2f."
      % (payment_amt))

Output¶

The payment due each year on the $100,000 loan is $-9367.88.