====== PV(rate, num_per, payment) ======
Category:  Number (Financial) function

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=====Description=====
This function calculates the present value of a loan or an investment, based on a constant interest rate.

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=====Additional syntax=====
Optional //future value// (fut_val) argument.
  pv(rate, num_per, payment, fut_val)
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Optional //payments due// (pay_due) argument.
  pv(rate, num_per, payment, fut_val, pay_due)

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=====Arguments=====
^Argument^Type^Description^
|rate|Number (decimal)|The interest rate of the loan (entered as a decimal).|
|num_per|Number|The number of payments of the loan (usually in months or years).|
|payment|Number (negative)|The payment made each period (that does not change), entered as a negative value.  Includes principal\\ and interest, but no fees or taxes.|
|fut_val|Number|Optional.  The future value, or cash balance, to be achieved after the last payment (i.e., "0" to pay the loan\\ off in full).  The default, if not supplied, is //0//.|
|pay_due|Binary (0 or 1)|Optional.  This value defines when payments are due.  Options:  //0// (the beginning of the period; default),\\ or //1// (the end of the period).|

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**Return value type:**  Number

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=====Remarks=====
For an accurate calculation, be sure to convert //rate// and //num_per// to the same time period.  If calculating a monthly payment and //rate// is an annual rate, divide it by 12 (//rate// / 12).  If //num_per// is given as years, multiply by 12 (//num_per// * 12).

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=====Examples=====
** Calculate the present value:**  Interest rate is 10% (annual), number of periods is 36 (months), payment is $225 per month.
  pv( (0.10/12), 36, -225) //Returns $6973.03 (months, rounded)
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** Calculate the present value:**  Interest rate is 14% (annual), payment is $6000 per year, final value is $30,000.
  pv(0.14, 10, -6000, 30000) //Returns $23,204.38 (rounded)
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** Calculate the present value:**  Interest rate is 1% (monthly), payment $600 per month, final value is $21,000, payments due at the end of the period.
  pv(0.01, 48, -600, 21000, 1) //Returns $9986.75 (rounded)

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===== See also =====
  * [[syntax:functions:fv|FV(rate, num_per, payment)]]
  * [[syntax:functions:nper|NPer(rate, payment, curr_val)]]
  * [[syntax:functions:ipmt|IPmt(rate, per, num_per, curr_val)]]
  * [[syntax:functions:pmt|Pmt(rate, num_per, curr_val)]]
  * [[syntax:functions:ppmt|PPmt(rate, num_per, curr_val)]]
  * [[syntax:functions:rate|Rate(num_per, payment, curr_val)]]