Annuity Due Formulas

Michael Brown

13 years ago

An annuity due is a series of annual payments made at the beginning of each year for a fixed number of years. Annuity due formulas are used to calculate annuity due values. The formula to use will depend on which components of the annuity due are already known.

Annuity Due Formula Examples

The listing below summarizes the various formulas to use for annuity due calculations.

In all annuity due formulas the following symbols are used.

FV = Future value
PV = Present value
i = Periodic rate
Pmt = Periodic payment
n = Number of years
LN is a natural logarithm

The example used below for each annuity due formula is based on the following information.

Future value = FV = 7,922.80
Present value = PV = 4,992.71
Annual annuity rate = i = 8%
Annual annuity payment = Pmt = 1,000
Number of years = n = 6

Future Value of an Annuity Due

Formula
FV = Pmt x ((1+i)ⁿ-1)/i x (1+i)

Excel Formula
FV = -FV(i%,n,Pmt,,1)

Example
FV = 1000 x ((1+8%)⁶-1)/8% x (1+8%) = 7,922.80

Present Value of Annuity Due

Formula
PV = Pmt x ((1-1/(1+i)ⁿ)/i x (1+i))

Excel Formula
PV = -PV(i%,n,Pmt,,1)

Example
PV = 1000*((1-1/(1+8%)⁶)/8% * (1+8%)) = 4,992.71

Calculate Annuity Due Payments based on Present Value

Formula
Pmt = PV/((1-1/(1+i)ⁿ)/i x (1+i))

Excel Formula
Pmt = PMT(i%,n,-PV,,1)
Example
Pmt = 4,992.71/((1-1/(1+8%)^6)/0.08 * (1+8%)) = 1,000

Calculate Annuity Due Payment based on Future Value

Formula
Pmt = FV/(((1+i)ⁿ-1)/i x (1+i))

Excel Formula
Pmt = PMT(i%,n,,-FV,1)

Example
Pmt = 7,922.80/(((1+8%)⁶-1)/8% * (1+8%)) = 1,000

Number of years based on Future Value of Annuity Due

Formula
n = LN(FV x i/(Pmt x (1+i))+1)/LN(1+i)

Excel Formula
n = NPER(i%,Pmt,,-FV,1)

Example
n = LN(7,922.80 x 8%/(1000 x (1+8%))+1)/LN(1+8%) = 6

Number of years based on Present Value of Annuity Due

Formula
n = -LN(1+i x (1-PV/Pmt))/LN(1+i)+1

Excel Formula
n = NPER(i%,Pmt,-PV,,1)

Example
n = -LN(1+8%*(1-4,992.71/1000))/LN(1+8%)+1 = 6

The annuity due formulas are summarized below.

The other type of annuity is the regular annuity where payments are made at the end of each year.

Last modified December 11th, 2019 by Michael Brown

About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.