Chapter 12
Annuities
Student Performance Objectives:
Section I Future Value of an Annuity: Ordinary and Annuity Due
12-1 Calculating the Future Value of an Ordinary Annuity by Using Tables
Section II Present Value of an Annuity
12-4 Calculating the Present Value of an Ordinary Annuity by Using Tables
Section III Sinking Funds and Amortization
12-7 Calculating the Amount of a Sinking Fund Payment by Table
12-8 Calculating the Amount of an Amortization Payment by Table
Chapter Notes, Teaching Tips and Lecture Launchers
• Lecture Launcher: Ask students when they plan to retire, what they plan to do when they
retire, and how much money they think they’ll need to have for the kind of retirement they’ll
• Lecture Launcher: Ask students which strategy would result in a higher amount at age 65:
• Saving $250 a month at 10% in a tax-deferred or tax-exempt investment from age 22
• Spotlight: Use Exhibit 12-1, Present and Future Value Time Lines, to help illustrate that an
annuity is a “series” of payments, whereas in Chapter 11, Compound Interest, we dealt with
only one payment, the beginning principal.
• For easy reference, remind students that all of the formulas used in this chapter are listed in
the Summary Chart at the end of the chapter.
• Spotlight: This chapter’s Business Decision, “Time is Money,” at the end of the chapter, is a
good lesson on how when money is invested can affect long range planning in business.
• Homework Activity: This chapter provides a good foundation for a discussion of IRAs and
other retirement plans.
• Have students research the various types of these plans, including their current rules
and regulations. Have them report their findings to the class.
• Spotlight: Invite a stockbroker or an insurance agent to class to speak to the students about
Section I Future Value of an Annuity: Ordinary and Annuity Due
• The word annuity is new to many students. Be sure they understand, an annuity is nothing
more than a series of payments or receipts of equal amounts of money per period for a
specified amount of time.
• Spotlight: Remind students, when calculating the future value of an annuity due, they must
• The most difficult concept for students to understand in this chapter is the difference between
ordinary annuities and annuities due.
• I use a time-line to illustrate that the interest earned with an annuity due investment is
higher than that of an ordinary annuity investment, because it starts earning interest
from the “beginning” of the first period, not the “end.”
• Spotlight: Point out to students that the interest earned with an annuity due is higher
than that of an ordinary annuity because the annuity due starts earning interest from
• Another way to illustrate the difference between an ordinary annuity and an annuity due is to
look at it from the perspective of a series of payments “going out.”
• Use a mnemonic device to help students remember which one is which. For example, rent
and mortgage payments are due at the beginning of the month, while ordinarily we wait
until the end of the year to fund our IRA’s – not a good idea!
Section II Present Value of an Annuity
• Students should recognize, the present value of an annuity is the “lump sum” amount of
money that must be deposited today, in order to provide a specified series of equal payments
(annuity) in the future.
• Spotlight: Remind students, when calculating the present value of an annuity due, they must
• Subtract one period from the number of periods, and
• Add 1.00000 to the table factor.
• Classroom Activity: This chapter provides a good opportunity for a discussion of IRAs and
other retirement plans that involve annuities.
Section III Sinking Funds and Amortization
• Have students keep in mind the difference between a sinking fund and amortization.
• A sinking fund is like a savings account. It is an account used to set aside equal
• Be sure students are aware that all sinking fund and amortization annuities in this section are
ordinary, with payments made at the end of the period.
• Spotlight: Be sure students recognize, in Section I and Section II of this chapter, the amount
• Collaborative Learning Activity To demonstrate their understanding of the subject, ask
students to break into small groups to write and solve some sinking fund and amortization
• Classroom Activity: Have students research and report to the class about the current, and
past few years’, rates of inflation. Ask them what their sources were. This may help those
students who could not find the information.
• Classroom Activity: Have students calculate how much they need to start saving for
retirement.
• Start by having them calculate how much in today’s dollars they want to have per
year when they retire.
Questions Students Always Ask
“Why do we add a period and subtract 1 from the table factor for annuities due?”
• The annuities tables are based on ordinary annuities, with payments made at the end
“How do I know if it’s an ordinary annuity or an annuity due?”
• Read the question carefully. Look for words that indicate the timing of the payments.
“What do I multiply the factor by?”
• One annuity payment. The fact that there are number of payments in an annuity
“The present value of this annuity seems too high; can this be right?”
• Ask yourself, if I put away this much money today, how much will it pay out over
“How do I know if a problem is a sinking fund, instead of an annuity?”
• Ask yourself what you know. If you know the periodic payment and want to find out
“I still don’t understand how to figure out the difference between lump sums and annuities,
present value or future value, ordinary annuity or annuity due!”
• Draw a timeline with several periods. Indicate with question marks and dollar signs
what you’re trying to find and when the payments occur. Then indicate which table
to use.
0 1 2 3
|__________|__________|__________| Table