Function InvestmentConstantInterestPayment(PresentValue, FutureValue, NumberPeriods, Period, InterestRate, Type)

InvestmentConstantInterestPayment

The function InvestmentConstantInterestPayment returns the interest payment of the specified period 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 repayment.

InvestmentConstantInterestPayment(
    PresentValue,            ! (input) numerical expression
    FutureValue,             ! (input) numerical expression
    NumberPeriods,           ! (input) numerical expression
    Period                   ! (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.

Period

The period for which you want to compute the interest payment. Period must be an integer in the range \(\{1, NumberPeriods + Type \}\). When \(Type = 1\), the extra period is to account the interest over the former period.

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 InvestmentConstantInterestPayment returns the interest payment for the specified period.

Equation

The interest payment \(i_i\) in period \(i\) is computed through the equation

\[i_i = -v_pr(1+r)^{i-1-T} - p\left(\left((1+r)^{i-1-T}-1\right)(1+r)^T+rT\right)\]

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 InvestmentConstantInterestPayment is similar to the Excel function IPMT.

See also

General equations for investments with constant, periodic payments.