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

InvestmentConstantPrincipalPayment

The function InvestmentConstantPrincipalPayment returns the principal 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 payment.

InvestmentConstantPrincipalPayment(
    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 InvestmentConstantPrincipalPayment returns the principal payment for the specified period.

Equation

The principal payment \(p_i\) in period \(i\) follows from the relation

\[p_i = p - i_i\]

where \(i_i\) is the interest payment in period \(i\).

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 InvestmentConstantPrincipalPayment is similar to the Excel function PPMT.

Example

How much is paid off for a loan of ten years and an interest of 4% in each period:

_p_life := 10 ;
_bp_type := 1;
_s_periods := ElementRange(1, _p_life + _bp_type);
_p_PrincipalPayment(_i_per) :=
        InvestmentConstantPrincipalPayment(
                PresentValue  :  100,
                FutureValue   :  0,
                NumberPeriods :  10,
                Period        :  _i_per,
                InterestRate  :  0.04,
                type          :  _bp_type);
block where single_column_display := 1, listing_number_precision := 8 ;
        display _p_PrincipalPayment;
endblock ;

The following table that the pay off portion of each anuity increases:

_p_PrincipalPayment := data
{  1 : -1.18548985e+01,
   2 : -8.32909443e+00,
   3 : -8.66225821e+00,
   4 : -9.00874854e+00,
   5 : -9.36909848e+00,
   6 : -9.74386242e+00,
   7 : -1.01336169e+01,
   8 : -1.05389616e+01,
   9 : -1.09605201e+01,
  10 : -1.13989409e+01,
  11 : -4.44089210e-15 } ;

Except for the first period; there is no interest to be paid when no time is passed.

References

• General equations for investments with constant, periodic payments.