Function InvestmentConstantRateAll(PresentValue, FutureValue, Payment, NumberPeriods, Type, Mode, NumberSolutions, Solutions)

InvestmentConstantRateAll

The procedure InvestmentConstantRateAll returns the interest rate(s) for an investment based on periodic, constant payments and a constant interest rate.

InvestmentConstantRateAll(
    PresentValue,            ! (input) numerical expression
    FutureValue,             ! (input) numerical expression
    Payment,                 ! (input) numerical expression
    NumberPeriods,           ! (input) numerical expression
    Type,                    ! (input) numerical expression
    Mode,                    ! (input) numerical expression
    NumberSolutions,         ! (output) numerical expression
    Solutions                ! (output) one-dimensional parameter
    )

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.

Payment

The periodic payment for the investment. Payment must be a real number.

NumberPeriods

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

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.

Mode

Indicates whether all the solutions need to be found or just one. \(Mode = 0\): the search for solutions stops after one solution is found. \(Mode = 1\): the search for solutions continues till all solutions are found.

NumberSolutions

The number of solutions found. If \(Mode = 0\) NumberSolutions will always be \(1\).

Solutions

There is not always a unique solution for InterestRate. Dependent on Mode one solution or all the solutions will be given. Solutions smaller than \(-1\) are not supposed to be relevant, so the search for solutions is limited to the area greater than \(-1\).

Note

• When you want to use this procedure in an objective function or constraint you have to use InvestmentConstantRate.

• The function InvestmentConstantRateAll is similar to the Excel function RATE.

Example

Given the local declarations:

Parameter _p_noSol;
Set _s_solutionNumbers {
    SubsetOf: Integers;
    Index: _i_solNo;
}
Parameter _p_sols {
    IndexDomain: _i_solNo;
}

All solutions to InvestmentConstantRate can be obtained using

_s_solutionNumbers := ElementRange(1,100);
InvestmentConstantRateAll(
    PresentValue    :  -100,
    FutureValue     :  0,
    Payment         :  10,
    NumberPeriods   :  13,
    type            :  0,
    Mode            :  1,
    NumberSolutions :  _p_noSol,
    Solutions       :  _p_sols );
block where single_column_display := 1, listing_number_precision := 6 ;
    display _p_noSol, _p_sols ;
endblock ;

In this particular example there is only one solution:

_p_noSol := 1 ;


_p_sols := data
{ 1 : 0.039769 } ;

References

• General equations for investments with constant, periodic payments.