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

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/Pmt))/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 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.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for 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.