- 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 functionRATE
.
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.