2.0 Introduction

Chapter Learning Objectives

By the end of the chapter you should be able to:

• Understand terminology associated with annuities
• Classify annuities based on the frequency of the payments and the compounding frequency
• Calculate the future value of an ordinary annuity
• Calculate the future value of an annuity due
• Calculate the present value of an ordinary annuity
• Calculate the present value of an annuity due
• Calculate the payment for an annuity
• Calculate the number of payments in an annuity
• Calculate the term of an annuity
• Calculate the interest rate for an annuity
• Solve problems involving a deferred annuity
• Solve problems involving a perpetuity

Payments show up everywhere. For example, you make payments on bank loans or you make payments into your RRSP. An annuity is anything where you make regularly scheduled payments. Here are some real-world examples of annuities.

• Last week you completed the purchase of your $\150,000$ starter home and finished all of the paperwork on your mortgage with the bank. You snagged a great mortgage rate of $5\%$ compounded semi-annually, locking it in for a five-year term with monthly payments of $\872.41$ (for the next 25 years) starting one month after you move in.
• You excitedly cruise to the Honda dealership to pick up your new $\22,475$ Honda Civic Sport, on which you have a four-year lease. Pulling out your iPhone (for which you pay $\60$ monthly), you ensure that you have enough funds in your chequing account to make the $\2,000$ down payment today along with the first of your $\242.16$ monthly lease payments at $2.9\%$ compounded monthly.
• Driving away in your Civic, you stop in at Sleep Country Canada and purchase a queen size mattress for your new bedroom. You recall a TV ad promoting an $\895$ Sealy mattress plus $12\%$ taxes with no money down and 12 easy, interest-free monthly payments of $\83.53$. It will be nice to have a comfortable bed to sleep in!

This chapter explores the concept of making regular payments toward savings goals or debt extinguishment. First, it introduces key payment concepts and reviews different types of payment plans. You will then calculate the future and present value of a stream of payments. You extend the application of the concepts further to solve for other variables such as the payment amount, the term, and the nominal interest rate.