Show the annuity formula with an example. An annuity can be calculated using the formula: \[ PV = PMT \times \left( \dfrac{(1 - (1 + r)^{-n})}{r} \right) \] where: PV = Present Value of the annuity

PMT = Payment amount per period
r = Interest rate per period
n = Number of periods

Example:
Let's say you are considering investing in an annuity that pays $1,000 per month for 5 years with an interest rate of 5% per year. You want to calculate the present value of this annuity.

PMT = $1,000
r = 5% or 0.05
n = 5 years

Using the formula:
\[ PV = $1,000 \times \left( \dfrac{(1 - (1 + 0.05)^{-5})}{0.05} \right) \]

\[ PV = $1,000 \times \left( \dfrac{(1 - (1.05)^{-5})}{0.05} \right) \]

\[ PV = $1,000 \times \left( \dfrac{(1 - 0.7835)}{0.05} \right) \]

\[ PV = $1,000 \times \left( \dfrac{0.2165}{0.05} \right) \]

\[ PV = $1,000 \times 4.33 \]

\[ PV = $4,330 \]

Therefore, the present value of the annuity that pays $1,000 per month for 5 years with an interest rate of 5% per year is $4,330.

Annuity Formula:

```
PV = PMT x [(1 - (1 + r)^-n) / r]
```

Where:

- PV = Present Value of the annuity
- PMT = Periodic payment amount
- r = Interest rate per period
- n = Number of periods

Example:

Let's say you want to calculate the present value of an annuity that pays $100 every year for the next 10 years. The interest rate is 5%.

Using the formula:

```
PV = PMT x [(1 - (1 + r)^-n) / r]
PV = 100 x [(1 - (1 + 0.05)^-10) / 0.05]
PV = 100 x [(1 - (1.05)^-10) / 0.05]
PV = 100 x [(1 - 0.61391) / 0.05]
PV = 100 x [0.38609 / 0.05]
PV = 100 x 7.7218
PV = $772.18
```

Therefore, the present value of the annuity is $772.18.