Related Functions:

The PV function calculates the Present Value of an investment, based on a series of future payments.

### Syntax

=PV(rate,nper,[pmt],[fv],[type])

#### Arguments

Argument Description
rate The interest rate, per period
nper The number of periods for the lifetime of the annuity or investment
[pmt] Optional. Specifies the payment per period. If omitted:

 • the [fv] argument must be supplied
[fv] Optional. Specifies the future value of the annuity, at the end of nper payments. If omitted:

 • it takes on the default value 0
[type] Optional. Defines whether the payment is made at the start or the end of the period. The [type] argument can have the value 0 or 1, meaning:

 0 – the payment is made at the end of the period 1 – the payment is made at the beginning of the period If omitted, the [type] argument takes on the default value of 0, denoting payments made at the end of the period.

#### Examples

##### Example 1

The following spreadsheet shows the PV function used to calculate the present value of an annuity that pays \$1,000 per month for a period of 5 years. The interest is 5% per year and each payment is made at the end of the month.

A B C D
1 Data
2 \$1,000 Periodic payment – monthly
3 8% Annual interest rate
4 20 Term – years
5
6 Formula Result Notes
7 =PV(A3/12,A4*12,A2) -\$119,554.29 Present value of an annuity with the terms in A2:A4, [type] omitted defaults to 0
8 =PV(A3/12,A4*12,A2,,1) -\$120,351,32 Present value of an annuity with the terms in A2:A4, payment made at the beginning of the period ([type] = 1)

Note: In the example:

• the annual interest rate of 8% had to be converted into a monthly rate (=8%/12), and
• the number of years had to be converted into months (=20*12)
• [fv] was not required in either formula

Cash Flow Convention: In line with general cash flow conventions, outgoing payments are represented by negative numbers and incoming payments are represented by positive numbers.

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the supplied arguments are non-numeric
Result is much higher or much lower than expected Usually occurs due to failure to convert the rate or the nper to months or quarters, i.e.:

 months = 12 * years monthly rate = annual rate/12 quarters = 4 * years quarterly rate = annual rate/4