PV

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

Returns the present value of a series of equal cash flows at regular intervals.

rate	The fixed interest rate per period.
nper	The total number of payments.
pmt	The fixed payment made each period.
fv	(Optional) The future value (or cash balance) after all the payments.
type	(Optional) The number indicating when the payments are due: 0 = the end of the period (default) 1 = the start of the period

REMARKS

* For an illustrated example refer to the Compounding Interest page.
* This function allows you to calculate the present value of a simple annuity.
* A negative number represents any cash you pay out.
* A positive number represents any cash you receive (start with or end with).
* The "rate" and "nper" MUST be expressed in the same units of time: years, months or days.
* The "rate" can be entered with a percentage sign or as a decimal.
* The "nper" is the number of compounding periods.
* The "pmt" argument typically contains principal and interest but no other fees or taxes.
* The "pmt" is the fixed payment made each period.
* If "fv" is left blank, then 0 is used.
* If "fv" is left blank, then you must include "pmt".
* If "pmt" is left blank, then you must include "fv".
* If "pmt" is left blank, then 0 is used.
* The "type" argument is irrelevant when "pmt" is left blank.
* If "type" is left blank, then 0 is used.
* If "type" = 0, then payments are made in arrears.
* You can use the FV function to return the future value for a series of equal cash flows at regular intervals.
* You can use the NPER function to return the number of periods for an investment.
* You can use the PMT function to return the full amount (principal + interest) paid every period on a loan with fixed interest.
* You can use the RATE function to return the interest rate for a series of equal cash flows at regular intervals.
* You can use the NPV function to calculate the net present value of a series of unequal cash flows at regular intervals.
* You can use the XNPV function to return the net present value of a series of unequal cash flows at irregular intervals.
* The equivalent VBA function is VBA.PV
* For the Microsoft documentation refer to support.microsoft.com
* For the Google documentation refer to support.google.com

	A
1	=PV(10%, 4, , 10000) = -$6,830.13
2	=PV(10%, 4, 0, 10000, 0) = -$6,830.13
3	=PV(10%, 4, 0, 10000, 1) = -$6,830.13
4	=FV(10%, 4, 0, -6830.135) = $10,000
5	=PV(0.1/12, 4*12, , 10000) = -$6,714.32
6	=FV(0.1/12, 4*12, 0, -6714.32) = $10,000
7	=PV(0.056, 2, , -10000) = $8,967.52
8	=PV(1%, 2*12, , -10000) = $7,875.66
9	=PV(0.045/12, 20*12, -1500, 500000, 0) = $33,470.85
10	=PV(12, 10, 10*100, 100, 0) = -$83.33
11	=PV(12/2, 102, 10/2100, 100, 0) = -$83.33
12	=PV(12/12, 1012, 10/12100, 100, 0) = -$83.33

1 - What is the present value of receiving £10,000 in 4 years time if the discount rate is 10% (compounded annually) with payments at the end of the period.
2 - What is the present value of receiving £10,000 in 4 years time if the discount rate is 10% (compounded annually) with payments at the end of the period.
3 - What is the present value of receiving £10,000 in 4 years time if the discount rate is 10% (compounded annually) with payments at the start of the period. The fixed payment is zero so the "type" argument makes no difference.
4 - This is checking the answer in 1,2 and 3.
5 - What is the present value of receiving £10,000 in 4 years time if the annual discount rate is 10% (compounded monthly).
6 - This is checking the answer is 3.
7 - What would my original amount have been if I have £10,000 in my account now and the annual growth rate was 5.6% over the past 2 years (compounded annually).
8 - What would my original amount have been if I have £10,000 in my account now and the annual growth rate was 1% a month over the past 2 years (compounded annually).
9 - How much would my deposit have to be if I wanted to have saved £500,000 after 20 years if I save £1,500 at the end of every month with an annual growth rate of 4.5%.
10 - What is the price of a 10 year bond with a par value of £100 and a coupon of 10% paid annually. Lets assume the discount rate is 12%. The result is negative as this is how much you will have to pay.
11 - What is the price of a 10 year bond with a par value of £100 and a coupon of 10% paid semi annually. Lets assume the discount rate is 12%.
12 - What is the price of a 10 year bond with a par value of £100 and a coupon of 10% paid monthly.