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

FormulaFV = Pmt x ((1+i)^{n}-1)/i x (1+i)Excel FormulaFV = -FV(i%,n,Pmt,,1)ExampleFV = 1000 x ((1+8%)^{6}-1)/8% x (1+8%) = 7,922.80

## Present Value of Annuity Due

FormulaPV = Pmt x ((1-1/(1+i)^{n})/i x (1+i))Excel FormulaPV = -PV(i%,n,Pmt,,1)ExamplePV = 1000*((1-1/(1+8%)^{6})/8% * (1+8%)) = 4,992.71

## Calculate Annuity Due Payments based on Present Value

FormulaPmt = PV/((1-1/(1+i)^{n})/i x (1+i))Excel FormulaPmt = PMT(i%,n,-PV,,1)ExamplePmt = 4,992.71/((1-1/(1+8%)^6)/0.08 * (1+8%)) = 1,000

## Calculate Annuity Due Payment based on Future Value

FormulaPmt = FV/(((1+i)^{n}-1)/i x (1+i))Excel FormulaPmt = PMT(i%,n,,-FV,1)ExamplePmt = 7,922.80/(((1+8%)^{6}-1)/8% * (1+8%)) = 1,000

## Number of years based on Future Value of Annuity Due

Formulan = LN(FV x i/(Pmt x (1+i))+1)/LN(1+i)Excel Formulan = NPER(i%,Pmt,,-FV,1)Examplen = 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

Formulan = -LN(1+i x (1-PV/1000))/LN(1+i)+1Excel Formulan = NPER(i%,Pmt,-PV,,1)Examplen = -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.

Last modified November 6th, 2016