### Table of Contents

# PV(rate, num_per, payment)

Category: Number (Financial) function

## Description

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

## Additional syntax

Optional *future value* (fut_val) argument.

pv(rate, num_per, payment, fut_val)

Optional *payments due* (pay_due) argument.

pv(rate, num_per, payment, fut_val, pay_due)

## 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). |

**Return value type:** Number

## 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).

## 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)

** 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)

** 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)