Copyright © 2008, The McGraw-Hill Companies, Inc.
- You deposit $3,000 each year into an investment account that earns 7.5% interest for 25 years.
a) Find n.
b) Find i (expressed as either a fraction or a decimal).
c) Find the value of s _n (^) | (^) i.
d) Find the future value of the annuity.
8. a. Calculate s _n (^) | (^) i if n 60 and i .03.
b. Use your answer from (a) to fi nd the future value of $500 invested at the end of each year for 60 years, assuming
a 3% interest rate.
c. Use your answer from (a) to fi nd the future value of $500 invested at the end of each quarter for 15 years,
assuming a 12% interest rate.
- Donni has decided to invest $2,000 each year in an account that she expects to earn 8.25%. If she keeps this up for
35 years, how much would she end up with in her account? - Find the future value of $857.35 per year for 20 years at 6½%.
- Saint Viateur College does not have much of an endowment,^1 and the college’s administration has developed a
multiyear plan to build it up by appealing to their alumni for contributions. The administration believes that it can raise
$800,000 in each of the next 7 years, and can invest this money at 7.3%. If it is successful, how much will the plan have
raised at the end of the 7 years? - Suppose I deposit $5,000 each year into a retirement account. (a) How much will I have in 40 years if my account
earns 5%? (b) How much will I have in 40 years if my account earns 10%?
C. Future Values for Nonannual Ordinary Annuities- Calculate s __ 72 | (^). 082
⁄ 12
as follows.
a. Write the annuity factor formula, plugging in the appropriate values for n and i.
b. Evaluate the formula by following the calculator steps shown below and fi lling in the values in the Result column of
the table below.
Operation Result
(1.082/12)^72
1
/(.082/12)
Exercises 4.2 159
(^1) An endowment is a fund owned by an organization such as a college, charity, church, hospital, or similar organization that is invested and used to support the
organization’s mission. Colleges, for example, might use their endowments to provide scholarships, keep tuitions lower, build better facilities, or fund research.