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

## 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.