Function InvestmentConstantRate(PresentValue, FutureValue, Payment, NumberPeriods, Type, LowerBound, UpperBound, Error)

InvestmentConstantRate

The function InvestmentConstantRate returns the interest rate for an investment based on periodic, constant payments and a constant interest rate. This function uses the procedure InvestmentConstantRateAll to determine all possible interest rates and returns the interest rate that is within the specified bounds.

InvestmentConstantRate(
    PresentValue,            ! (input) numerical expression
    FutureValue,             ! (input) numerical expression
    Payment,                 ! (input) numerical expression
    NumberPeriods,           ! (input) numerical expression
    Type,                    ! (input) numerical expression
    [LowerBound,]            ! (optional) numerical expression
    [UpperBound,]            ! (optional) numerical expression
    [Error]                  ! (optional) 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.

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.

LowerBound

Indicates a minimum for the interest rate to be accepted by this function. The default is \(-1\).

UpperBound

Indicates a maximum for the interest rate to be accepted by this function. The default is \(5\).

Error

Indicates whether AIMMS should give an error if multiple solutions are found that satisfy the bounds. \(Error = 0\): if multiple solutions are found, return the solution with the smallest absolute value. \(Error = 1\): if multiple solutions are found, return an error message. The default is \(0\).

Return Value

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

Note

• The function InvestmentConstantRate can be used in an objective function or constraint. The input parameters PresentValue, FutureValue and Payment can be used as variables.

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

Example

InvestmentConstantRate is used when there is a fixed series of equal payments to determine the interest percentage needed to make up for a loan or to save up for an investment.

! Which interest rate do I need to save up for a given investment
! with a given series of fixed savings?
_p_pctSavingUp :=
        InvestmentConstantRate(
                PresentValue  :  0,
                FutureValue   :  -100,
                Payment       :  10,
                NumberPeriods :  8,
                type          :  0,
                LowerBound    :  -1,
                UpperBound    :  5,
                Error         :  1);

! With which percentage can I pay off a loan,
! given a fixed series of equal payments?
_p_pctReimburse :=
        InvestmentConstantRate(
                PresentValue  :  -100,
                FutureValue   :  0,
                Payment       :  10,
                NumberPeriods :  13,
                type          :  0,
                LowerBound    :  -1,
                UpperBound    :  5,
                Error         :  1);

block where single_column_display := 1, listing_number_precision := 6 ;
        display { _p_pctSavingUp, _p_pctReimburse};
endblock ;

As the number of periods used are not equal, it is hard to compare the results.

_p_pctSavingUp  := 0.062870 ;
_p_pctReimburse := 0.039769 ;

References

• General equations for investments with constant, periodic payments.