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CHAPTER 4
SUMMARY
Topic Key Ideas, Formulas, and Techniques Examples
Annuities, Their Uses, and
Te rminology, pp. 141–143Any series of regular payments can be analyzed as
an annuity. Key terms: present value, future value,
ordinary annuity, annuity due.See discussion in Chapter 4.1The Future Value of an
Ordinary Annuity, p. 149- The Future Value Ordinary Annuity
Formula: FV PMT s _n (^) | (^) i
• s _n (^) | (^) i is the future value annuity factor.
- The annuity factor may be found from tables,
calculator/computer programs, or formulas.
How much will I have as a
future value if I deposit $3,000
at the end of each year into an
account paying 6%?
(Example 4.2.1)The Future Value Annuity
Factor Formula, pp. 153–154• s _n (^) | (^) i
(1 i )n 1
___i
- n is the number of time periods, i is the interest
rate per period.
Find the future value annuity
factor for a monthly annuity
with a 15-year term and a
7.1% interest rate.
(Example 4.2.5)
Finding Total Interest Earned,
pp. 154–155- To fi nd the total interest earned in an annuity,
subtract the total payments from the future
value.
Carrie deposits $250 each
month into an account paying
4.5% for 5 years. How much
interest does she earn?
(Examples 4.2.6 and 4.2.7)The Future Value of an
Annuity Due, p. 156- The Future Value Annuity Due
Formula: FV PMT s _n (^) | (^) i (1 i)
- The calculation is done the same way as an
ordinary annuity’s, but then multiply by (1 i) at
the end.
Mariano deposits $2,500
at the start of each year at
8 1 / 4 %. How much will he have
after 40 years. (Example 4.2.8)Sinking Funds, p. 163 • A sinking fund is just an annuity whose
payments are determined by the desired future
value.- Use the future value annuity formula, fi nd the
annuity factor, and then use algebra to fi nd the
payment amount.
How much should Shauna
set aside at the start of
each quarter to accumulate
$10,000 in 2 years, assuming
her account earns 4.8%?
(Example 4.3.2)Sinking Funds and Retirement
Planning, p. 160- To accumulate a large future value, the period of
time makes an enormous difference in the size
of the payments needed.
To accumulate $1,000,000 by
age 70, how much would Joe
need to deposit semimonthly
assuming he starts at age
65, 50, 35, 25, 18, or age 2?
(Example 4.3.6)
The Present Value of an
Ordinary Annuity, p. 169- The Present Value Ordinary Annuity
Formula: PV PMT a _n (^) | (^) i
• a _n (^) | (^) i is the future value annuity factor
- The annuity factor may be found from tables,
calculator/computer programs, or formulas.
How much can you afford to
borrow on a car loan if your
payments will be $275 per
month for 3 years at 6%.
(Example 4.4.2)The Present Value Annuity
Factor Formula, pp. 173–174• a _n (^) | (^) i
s _n (^) | (^) i
_(1 i)n
• a _n (^) | (^) i 1 ^ (1^ ^ i)
n
__i
- Either formula can be used; both give the same
results.
Find the present value annuity
factor for a 5-year annuity with
quarterly payments and a 9%
interest rate. (Example 4.4.6)(Continued)