224 RATEOF RETURNANALYSIS
7-13 Compute the rate of return for the following cash flow.
Year Cash Flow
o -$500
1-3 0
4 +4500
7-14 A woman went to the Beneficial Loan Company and
borrowed $3000. She must pay $119.67 at the end of
each month for the next 30 months.
(a) Calculate the nominal annual interest rate she is
paying to within ::1::0.15%.
(b) What effective annual interest rate is she paying?
7-15 Helen is buying a $12,375 automobile with a $3000
down payment, followed by 36 monthly payments
of $325 each. The down payment is' paid immedi-
ately, and the monthly payments are due at the end
of each month. What nominal annual interest rate is
Helen paying? What effective interest rate?
(Answers: 15%; 16.08%)
7-16 Peter Minuit bought an island from the Manhattoes
Indians in 1626 for $24 worth of glass beads and trin-
kets. The 1991 estimate of the value of land on this
island was $12 billion. What rate of return would the
Indians have received if they had retained title to the
island rather than selling it for $24?
7-17 A man buys a corporate bond from a bond brokerage
house for $925. The bond has a face value of $1000
and pays 4% of its face value each year. If the bond
will be paid off at the end of 10 years, what rate of
return will the man receive? (Answer:4.97%)
7-18 A well-known industrial firm has issued $1000 bonds
that carry a 4% nominal annual interest, rate paid
semiannually. The bonds mature 20 years from now,
at which time the industrial firm will redeem them
for $1000 plus the terminal semiannual interest pay-
ment. From the financial pages of your newspaper you
learn that the bonds may be purchased for $715 each
($710 for the bond plus a $5 sales commission). What
nominal annual rate of return would you receive if
you purchased the bond now and held it to maturity
20 years hence? (Answer:6.6%)7-19 One aspect of obtaining a college education is the
prospect of improved future earnings in comparison
to non-college graduates. Sharon Shay estimates that
a college education has a $28,000 equivalent cost at
graduation. She believes the benefits of her education
will occur throughout 40 years of employment. She
thinks that during the first 10 years out of college,
her income will be high~r than that of a non-college
-. ~ ,-graduate by $3000 per year. During the subsequent
10 years, she projects an annual income that is $6000
per year higher. During the last 20 years of employ-
ment, she estimates an annual salary that is $12,000
above the level of the non-college graduate. If her es-
timates are correct, what rate of return will she receive
as a result of her investment in a college education?
7-20 An investor purchased a one-acre lot on the outskirts
of a city for $9000 cash. Each year he paid $80 of
property taxes. At the end of 4 years, he sold the
lot. After deducting his selling expenses, the investor
received $15,000. What rate ofreturn did he receive
on his investment? (Answer: 12.92%)
7-21 A popular reader's digest offers a lifetime subscrip-'
tion to the magazine for $200. Such a subscnption
may be given as a gift to an infant at birth (the par-
ents can read it in those early years), or takenbut
by an individual for himself. Normally, the magazine.
costs $12.90 per year. Knowledgeable people say it
probably will continue indefinitely at this $12.90 rate..
What rate of return would be obtained if a life sub-
scription were purchased for an infant, rather than
paying $12.90 per year beginning immediately? You
may make any reasonable assumption!;, but the com-
pound interest factors must becorrectlyused.
7-22 On Apri12, 1988, an engineer bought a $1000 bond
of an American airline for $875. The bond paid 6%
on its principal amount of $1000, half in each of its
April 1 and October 1 semiannual payments; it repaid
the $1000 principal sum on October 1, 2001. What
nominal rate of return did the engineer receive from
the bond if he held it to its maturity (on October 1,
2001)? (Answer: 7.5%)
7-23 The cash price of a machine tool is $3500. The
dealer is willing to accept a $1200 down payment and
24 end-of-month monthly payments of $110 each. At
what effective interest rate are these terms equivalent?
(Answer: 14.4%)
7-24 A local bank makes automobile loans. It charges 4%
per year in the following manner: if$3600 is borrowed
to be repaid over a 3-year period, the bank interestcharge is $3600 x 0.04 x 3 years=$432. The bank
deducts the $432 of interest from the $3600 loan and
gives the customer $3168 in cash. The customer must
repay the loan by paying 1136 of $3600, or $100, at
the end of each month for 36 months. What nominal
annual interest rate is the bank actually charging for
this loan?--