# 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.

Annuity Due Formulas November 6th, 2016

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