Annuity Due Formulas

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 of the annuity due formulas 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/1000))/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 other type of annuity is the regular annuity where payments are made at the end of each year.

November 6, 2016