Function InvestmentConstantPeriodicPayment(PresentValue, FutureValue, NumberPeriods, InterestRate, Type)

InvestmentConstantPeriodicPayment

The function InvestmentConstantPeriodicPayment returns the periodic payment for an investment based on periodic, constant payments and a constant interest rate.

InvestmentConstantPeriodicPayment(
    PresentValue,            ! (input) numerical expression
    FutureValue,             ! (input) numerical expression
    NumberPeriods,           ! (input) numerical expression
    InterestRate,            ! (input) numerical expression
    Type                     ! (input) numerical expression
    )

Arguments

PresentValue

The total amount that a series of future payments is worth at this moment. PresentValue must be a real number.

FutureValue

The cash balance you want to attain after the last payment is made. FutureValue must be a real number.

NumberPeriods

The total number of payment periods for the investment. NumberPeriods must be a positive integer.

InterestRate

The interest rate per period for the investment. InterestRate must be a numerical expression in the range \((-1, 1)\).

Type

Indicates when payments are due. \(Type = 0\): Payments are due at the end of each period. \(Type = 1\): Payments are due at the beginning of each period.

Return Value

The function InvestmentConstantPeriodicPayment returns the periodic payment for the investment.

Note

• This function can be used in an objective function or constraint and the input parameters PresentValue, FutureValue and InterestRate can be used as a variable.

• The function InvestmentConstantPeriodicPayment is similar to the Excel function PMT.

Example

Perhaps the following will encourage you to save up first:

! How much needs to be paid per period,
! for 10 periods, and an interest rate of 4%
! to attain a capital of 100 in the end?
_p_constPeriodicPaymentSavingup := InvestmentConstantPeriodicPayment(
    PresentValue  :  0,
    FutureValue   :  100,
    NumberPeriods :  10,
    InterestRate  :  0.04,
    type          :  0);

! Spending a 100 now, how much do I have to
! reimburse/compensate over each of the 10 periods,
! whereby the interest rate is 4%
_p_constPeriodicPaymentReimbursing := InvestmentConstantPeriodicPayment(
    PresentValue  :  100,
    FutureValue   :  0,
    NumberPeriods :  10,
    InterestRate  :  0.04,
    type          :  0);

block where single_column_display := 1, listing_number_precision := 6 ;
    display { _p_constPeriodicPaymentSavingup, _p_constPeriodicPaymentReimbursing } ;
endblock ;

The result of this example shows there is a 50% difference in amount to be saved per period, if you spent it at the beginning or at the end:

_p_constPeriodicPaymentSavingup    :=  -8.329094 ;
_p_constPeriodicPaymentReimbursing := -12.329094 ;

References

• General equations for investments with constant, periodic payments.