Function InvestmentConstantCumulativeInterestPayment(PresentValue, FutureValue, NumberPeriods, StartPeriod, EndPeriod, InterestRate, Type)

# InvestmentConstantCumulativeInterestPayment

The function InvestmentConstantCumulativeInterestPayment returns the cumulative interest payment for the specified interval for an investment based on periodic, constant payments and a constant interest rate. Every periodic payment can be divided in two parts: an interest payment and a principal payment.

InvestmentConstantCumulativeInterestPayment(
PresentValue,            ! (input) numerical expression
FutureValue,             ! (input) numerical expression
NumberPeriods,           ! (input) numerical expression
StartPeriod,             ! (input) numerical expression
EndPeriod,               ! (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.

StartPeriod

The starting period of the interval for which you want to compute the cumulative interest payment. StartPeriod must be an integer in the range $$\{ 1, NumberPeriods \}$$.

EndPeriod

The ending period of the interval for which you want to compute the cumulative interest payment. EndPeriod must be an integer in the range $$\{ StartPeriod, NumberPeriods\}$$.

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 InvestmentConstantCumulativeInterestPayment returns the sum of the interest payments for the periods in the specified interval.

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 InvestmentConstantCumulativeInterestPayment is similar to the Excel function CUMIPMT.

## Example

How much of the payments during the first half of the loan is interest?

_p_interestFirstFiveYears :=
InvestmentConstantCumulativeInterestPayment(
PresentValue  :  10,
FutureValue   :  0,
NumberPeriods :  10,
StartPeriod   :  1,
EndPeriod     :  5,
InterestRate  :  0.1,
type          :  0);
block where single_column_display := 1, listing_number_precision := 6 ;
display _p_interestFirstFiveYears ;
endblock ;


That is significant:

_p_interestFirstFiveYears := -4.306601 ;


## References

• General equations for investments with constant, periodic payments.