**What Are Annuities?**

Annuities are essentially a series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed time period. The most common payment frequencies are yearly, semi-annually (twice a year), quarterly and monthly. There are two basic types of annuities: ordinary annuities and annuities due.

- Ordinary Annuity: Payments are required at the end of each period. For example, straight bonds usually pay coupon payments at the end of every six months until the bond's maturity date.
- Annuity Due: Payments are required at the beginning of each period. Rent is an example of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.

**Calculating the Future Value of an Ordinary Annuity**

If you know how much you can invest per period for a certain time period, the future value of an ordinary annuity formula is useful for finding out how much you would have in the future by investing at your given interest rate. If you are making payments on a loan, the future value is useful in determining the total cost of the loan.

Let's now run through Example 1. Consider the following annuity cash flow schedule:

C = Cash flow per period i = interest rate n = number of payments |

= $1000*[5.53] = $5525.63 |

**Calculating the Present Value of an Ordinary Annuity**

If you would like to determine today's value of a future payment series, you need to use the formula that calculates the present value of an ordinary annuity. This is the formula you would use as part of a bond pricing calculation. The PV of an ordinary annuity calculates the present value of the coupon payments that you will receive in the future.

C = Cash flow per period i = interest rate n = number of payments |

= $1000*[4.33] = $4329.48 |

**Calculating the Future Value of an Annuity Due**

When you are receiving or paying cash flows for an annuity due, your cash flow schedule would appear as follows:

= $1000*5.53*1.05 = $5801.91 |

**Calculating the Present Value of an Annuity Due**

For the present value of an annuity due formula, we need to discount the formula one period forward as the payments are held for a lesser amount of time. When calculating the present value, we assume that the first payment was made today.

We could use this formula for calculating the present value of your future rent payments as specified in a lease you sign with your landlord. Let's say for Example 4 that you make your first rent payment at the beginning of the month and are evaluating the present value of your five-month lease on that same day. Your present value calculation would work as follows:

= $1000*4.33*1.05 = $4545.95 |

**Conclusion**

Now you can see how annuity affects how you calculate the present and future value of any amount of money. Remember that the payment frequencies, or number of payments, and the time at which these payments are made (whether at the beginning or end of each payment period) are all variables you need to account for in your calculations.