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.