- 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 functionPPMT
.
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.