System.Power(Decimal, Decimal) Method
Version: Available or changed with runtime version 1.0.
Raises a number to a power. For example, you can use this method to square the number 2 to get the result of 4.
Syntax
NewNumber := System.Power(Number: Decimal, Power: Decimal)
Note
This method can be invoked without specifying the data type name.
Parameters
Number
Type: Decimal
The number you want to raise exponentially. This number is the base in the exponential method.
Power
Type: Decimal
The exponent in the exponential method.
Return Value
NewNumber
Type: Decimal
Example 1
var
Number1: Decimal;
Power1: Decimal;
Result1: Decimal;
Text000: Label '%1 raised to the power of %2 = %3';
begin
Number1 := 64;
Power1 := 0.5;
Result1 := Power(Number1, Power1);
Message(Text000, Number1, Power1, Result1);
end;
On a computer that has the regional format set to English (United States), the first message window displays the following:
64 raised to the power of 0.5 = 8
This example shows that raising a number to the power of 0.5 corresponds to the square root of the number.
Example 2
This example shows a typical use for the POWER method.
If a principal amount P is deposited at interest rate R and compounded annually, then at the end of N years, the accumulated amount (A) is:
A = P(1 + R)N
For example, you put LCY 2800 into a bank account that pays 5 percent, which is compounded quarterly. To determine what the amount will be in eight years, you must consider:
N = 32 payment periods (8 years times 4 quarterly periods)
R = 0.0125 per period (5 percent divided by 4 quarterly periods)
The accumulated amount A is:
A = LCY 2800(1 + 0.0125)32 =LCY 2800(1.4881) = LCY 4166.77
If a principal amount P is deposited at the end of each year at interest rate R (in decimal notation) compounded annually, then at the end of N years, the accumulated amount is:
A = P[((1 + R)N - 1)/R]
This is typically called an annuity.
For example, you have an annuity in which a payment of LCY 500 is made at the end of each year. The interest on this annuity is 4 percent, which is compounded annually. To determine what the annuity will be worth in 20 years, you must consider:
R = 0.04
N = 20
The amount of the annuity A will be:
A = LCY 500[((1 + 0.04)20 - 1)/0.04 = LCY 14,889.04
var
P: Decimal;
R: Decimal;
N: Decimal;
A: Decimal;
FormatString: Text;
Text000: Label 'Principal $%1 at a 5 percent interest rate is compounded quarterly.\\';
Text001: Label '(Rate = %2)\\';
Text002: Label 'The amount after %3 years = $%4.';
Text003: Label 'Principal $%1 is deposited at the end of each year at a 4 percent interest rate, compounded annually.\\';
Text004: Label '(Rate = %2)\\';
Text005: Label 'The amount after %3 years = $%4.';
begin
FormatString := '<Precision,2><Standard Format,1>';
// Example 1
P := 2800;
R := 0.0125;
N := 32;
A = P * (Power(1 + R, N));
Message(Text000 + Text001 + Text002, P, R, N, Format(A,0,FormatString);
// Example 2
P = 500;
R = 0.04;
N = 20;
A = P * ((Power(1 + R, N) - 1)/R);
Message(Text001, P, R, N, Format(A,0,FormatString));
end;
On a computer that has the regional format set to English (United States), the first message window displays the following:
Principal $2,800 at a 5 percent interest rate is compounded quarterly.
(Rate = 0.0125)
The amount after 32 years = $4166.77.
The second message window displays the following:
Principal $500 is deposited at the end of each year at a 4 percent interest rate, compounded annually.
(Rate = 0.04)
The amount after 20 years = $14889.04.