142 Chapter 4 Annuities
Rent payments (until the rent changes)
Pension or Social Security payments (as long as payments do not change)
“Budget plan” utility bills (same amount paid each month)
Regularly scheduled deposits to a savings program, such as an Individual Retirement
Account (an IRA)Some Examples That Are Not AnnuitiesMonthly credit card payments (unless you pay the same amount each month)
Your paycheck (if hours vary, or if paid on commission)
Daily receipts of a business
“Pay as you go” utility billsA few words of caution about terminology are in order. The term annuity can be used for a
type of insurance contract (including such variations as fixed annuities, variable annuities,
and tax-sheltered annuities). While these products often have features that involve a series
of payments that fits our definition, it is important not to confuse the annuities we are talk-
ing about with these types of insurance contracts. For clarity’s sake, we will use the term
insurance annuity when referring to these contracts, though you should be aware that in
the real world people are not always so clear and the plain “annuity” is generally used for
them. Fortunately, it is usually clear from context which sort of annuity one is talking about,
and the terminology doesn’t create any more confusion than the fact that Washington is the
name of both a city and a state.Present and Future Values of Annuities
In some situations, such as IRA deposits, the annuity payments are made for the purpose
of accumulating a sum of money at a future date. In others, such as a mortgage or car loan,
the payments are being made in exchange for a sum of money received at the start of the
annuity. In both cases, the sum of money involved is important enough to have a name
attached to it.Definitions 4.1.2
A sum of money to which an annuity’s payments and interest accumulate in the end is called
the annuity’s future value.A sum of money paid at the beginning of an annuity, to which the annuity’s payments are
accepted as equivalent, is called the annuity’s present value. (The present value is also
sometimes called the amount of the annuity.)Note that we already have used the terms present value and future value with compound
interest. Their meanings here are consistent with what these terms meant in the compound
interest sections: present value comes at the beginning, future value comes at the end.
Some examples will help illustrate these terms:Example 4.1.1 Distinguishing between present value and future value of an annuity.(a) Dylan deposits $25 from each paycheck into a 401(k) savings plan at work.
He will keep this up for the next 40 years, at which time he plans to retire,
hopefully having accumulated a large balance in his account. Since equal
payments are being made into the account at regular intervals, this is an annuity.
Is the value of the account when Dylan retires a present value or a future value?The value of the account when Dylan reaches retirement would be the future value.(b) Thalissa borrowed $160,000 to buy a house. To pay off this mortgage loan, she
agreed to make payments of $1,735.52 per month for 30 years. Since her mortgage- • • • • • • •