# Annuity Formulas

An annuity is a series of annual payments made at the end of each year for a fixed number of years. Annuities with payments at the end of each year are sometimes referred to as regular annuities.

## Annuity Formula Examples

Annuity formulas are used to calculate annuity values. The formula to use will depend on which components of the annuity are already known.

The listing below summarizes the various formulas to use for annuity calculations.

In all annuity 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 formulas is based on the following information.

• Future value = FV = 7,335.93
• Present value = PV = 4,622.88
• Periodic rate = i = 8%
• Periodic payment = Pmt = 1,000
• number of years = n = 6

## Future Value of an Annuity

```Formula
FV = Pmt x ((1+i)n-1)/i
Excel Formula
FV = -FV(i%,n,Pmt)
Example
FV = 1000 x ((1+8%)6-1)/8% = 7,335.93
```

## Calculate Annuity Payments based on Present Value

```Formula
Pmt = PV/((1-1/(1+i)n)/i)
Excel Formula
Pmt = PMT(i%,n,-PV)
Example
Pmt = 4,622.88/((1-1/(1+8%)6)/8%) = 1,000
```

## Calculate Annuity Payment based on Future Value

```Formula
Pmt = FV/(((1+i)n-1)/i)
Excel Formula
Pmt = PMT(i%,n,,-FV)
Example
Pmt = 7,335.93 /(((1+8%)6-1)/8%) = 1,000
```

## Number of years based on Future Value

```Formula
n = LN(1+FV/Pmt x i)/LN(1+i)
Excel Formula
n = nPER(i%,Pmt,,-FV)
Example
n = LN(1+7,335.93/1000 x 8%)/LN(1+8%) = 6
```

## Number of years based on Present Value

```Formula
n = -LN(1-PV/Pmt x i)/LN(1+i)
Excel Formula
n = nPER(i%,Pmt,-PV)
Example
n = -LN(1-4,622.88/1000 x 8%)/LN(1+8%) = 6
```

The other type of annuity is the annuity due where payments are made at the beginning of each year.

Annuity Formulas November 6th, 2016

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