# BM5.1 – Introduction to Annuity Types

Chapter 5, Lesson 1

In this lesson students will:

• be able to define what is meant by an annuity
• understand the difference between a simple and an ordinary annuity
• understand the difference between an ordinary annuity and an annuity due

## Annuities

#### Ordinary Annuities & Annuities Due

Financial problems involving making or receiving equivalent payments are quite common. In this chapter of our course we would like to understand how to work with problems involving equivalent payments. We refer to a financial problem dealing with equivalent payments over equal periods of time an annuity.

Annuities can be roughly sorted into four different types. The first way we sort an annuity problem is based on when the equivalent payment happens. During the payment period, the equivalent payment may occur either at the beginning or at the end of the period. For example, when considering rent payment, you may have to either pay your landlord at the beginning or the end of the month. This is an important factor since a payment happening at the beginning of the payment period will earn interest throughout the payment period; whereas one happening at the end will not.

An annuity problem in which the equivalent payment occurs at the beginning of the payment period is called an annuity due. Chapters 6 & 8 will cover annuity due problems. An annuity problem in which the equivalent payment occurs at the end of the payment period is called an ordinary annuity. Ordinary annuities are covered in Chapters 5 & 7.

#### Simple Annuities & General Annuities

The second way we sort an annuity problem is dependent on comparing two frequencies. Since an annuity problem involves compounding interest, the first frequency to keep in mind is the compound frequency, which we will refer to as $f_{1}$. The other frequency to keep in mind the the payment frequency, which we will refer to as $f_{2}$. For example, an RRSP account may give you a bi-weekly payment; yet earn interest at the end of every month (here, $f_{1}=12$ and $f_{2}=26$). This is a bit of a subtle problem and we will explore how to solve this technical issue in Section 7.1.

An annuity problem where the frequency of the equivalent payments and the frequency of the compounding periods is the same is referred to a simple annuity. Simple annuities are covered in Chapters 5 & 6. An annuity problem where the frequency of the equivalent payments and the frequency of the compounding periods are different is referred to a general annuity. Chapters 7 & 8 are dedicated to discussing general annuities.