`P = PV * (( r )/(1-(1+ r )^(- n )))* 1/(1+ r )`

Enter a value for all fields

The Annuity Due-Payment (PV) calculator computes the periodic payment (P) from a fixed rate (r) annuity that draws down the annuity to zero over a number of periods (n) (see Example below).

INSTRUCTIONS: Choose preferred currency units and enter the following:

• (PV)  This is the present value of the annuity.
• (r) This the interest rate per period.
• (n) This is the number of periods.

Annuity Payment: The calculator returns the periodic payment in U.S. dollars.  However this can be automatically converted to other currency units via the pull-down menu.

The  Math / Science

The annuity due-payment (PV) formula is used to calculate each installment of a series of cash flows or payments when the first installment is received immediately, using present value.  The formula is as follows:

`P = PV * ( r/(1-(1+r)^(-n))) * 1/(1+r)`

where:

• PV is the Present Value
• r is the interest rate per period
• n is the number of periods

Example:
A person has $60,000 in an annuity that is that they must eliminate through monthly withdraws in the next ten years.  So, PV would be $50,000.  Let's assume a 2% annual interest rate (r = 0.25% monthly), and 120 months (n).  The payment (P) is $577.92 per month.