Documentation/Calc Functions/PDURATION

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    Function name:

    PDURATION

    Category:

    Financial Analysis

    Summary:

    Calculates the number of compounding interest periods needed for an invested sum to increase to a desired value. The interest rate is assumed to be constant for all periods.

    Syntax:

    PDURATION(Rate; PV; FV)

    Returns:

    Returns a real number, which is the number of interest periods required for the initial sum to increase to the desired value, at the given interest rate.

    Note that for practical argument values (initial sum < desired value), PDURATION returns a positive number of periods. However, no error is returned if the initial amount is greater than or equal to the desired amount; in such cases the function could return 0 or a negative number.

    Arguments:

    Rate is a positive real number (expressed as a percentage, such as 2.5%, or a decimal fraction, such as 0.025), or a reference to a cell containing that number, which is the constant periodic interest rate.

    PV is a positive real number, or a reference to a cell containing that number, which is the initial amount invested.

    FV is a positive real number, or a reference to a cell containing that number, which is the desired future amount. FV must be in the same currency units as PV.

    • If any argument is non-numeric, then PDURATION reports a #VALUE! error.
    • If any argument is less than or equal to 0.0, then PDURATION reports an invalid argument error (Err:502).

    Additional details:

    • The formula for PDURATION is obtained by manipulating the standard periodic compound interest formula to determine the number of periods required. Thus:
    [math]\displaystyle{ \text{PDURATION}(Rate;\:PV;\:FV)~=~\frac{\log(\frac{FV}{PV})}{\log(1+Rate)} }[/math]
    • For more information about the periodic compound interest formula, visit Wikipedia’s Compound interest page.

    Examples:

    Formula Description Returns
    =PDURATION(A1; A2; A3) where cells A1:A3 contain the values 4.75%, 25000, and 40000 respectively. A sum of 25,000 currency units is invested at an annual interest rate of 4.75% and the investor wishes the value of the investment to increase to 40,000 currency units. The formula returns the value 10.1279975301661, indicating that the desired value will be exceeded after the eleventh interest period. 10.1279975301661
    =PDURATION(0.035; 10000; 12000) A sum of 10,000 currency units is invested at an annual interest rate of 3.5% and the investor wishes the value of the investment to increase to 12,000 currency units. The formula returns the value 5.29982544887, indicating that the desired value will be exceeded after the sixth interest period. 5.29982544887
    =PDURATION(4%; 5000; 10000) A sum of 5,000 currency units is invested at an annual interest rate of 4% and the investor wishes the value of the investment to double to 10,000 currency units. The formula returns the value 17.6729876851297, indicating that the desired value will be exceeded after the eighteenth interest period. This is an example of the so-called rule of 72 in action – simply divide the number 72 by the interest rate (72 ÷ 4 = 18 in this case) to obtain the approximate number of periods required for an invested sum to double. 17.6729876851297

    Related LibreOffice functions:

    DURATION

    MDURATION

    ODF standard:

    Section 6.12.35, part 2

    Related (or similar) Excel functions:

    PDURATION since v.2013.