- 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 functionIPMT
.
Example
How much interest is paid 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_InterestPayment(_i_per) :=
InvestmentConstantInterestPayment(
PresentValue : 100,
FutureValue : 0,
NumberPeriods : 10,
Period : _i_per,
InterestRate : 0.04,
type : _bp_type);
block where single_column_display := 1, listing_number_precision := 6 ;
display _p_InterestPayment;
endblock ;
The following table shows that the interest portion of each anuity becomes less:
_p_InterestPayment := data
{ 2 : -3.525804e+00,
3 : -3.192640e+00,
4 : -2.846150e+00,
5 : -2.485800e+00,
6 : -2.111036e+00,
7 : -1.721282e+00,
8 : -1.315937e+00,
9 : -8.943784e-01,
10 : -4.559576e-01,
11 : 4.440892e-15 } ;
References
General equations for investments with constant, periodic payments.