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Chapter 5: Time Value of Money M/C Problems Page 175
144. Suppose you are buying your first condo for $145,000, and you will make
a $15,000 down payment. You have arranged to finance the remainder
with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal
interest rate, with the first payment due in one month. What will your
monthly payments be?
a. $741.57
b. $780.60
c. $821.69
d. $862.77
e. $905.91
145. Your uncle will sell you his bicycle shop for $250,000, with “seller
financing,” at a 6.0% nominal annual rate. The terms of the loan would
require you to make 12 equal end-of-month payments per year for 4
years, and then make an additional final (balloon) payment of $50,000
at the end of the last month. What would your equal monthly payments
be?
a. $4,029.37
b. $4,241.44
c. $4,464.67
d. $4,699.66
e. $4,947.01
146. Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5
equal installments at the end of each of the next 5 years. How much
interest would you have to pay in the first year?
a. $1,200.33
b. $1,263.50
c. $1,330.00
d. $1,400.00
e. $1,470.00
147. You plan to borrow $35,000 at a 7.5% annual interest rate. The terms
require you to amortize the loan with 7 equal end-of-year payments.
How much interest would you be paying in Year 2?
a. $1,994.49
b. $2,099.46
c. $2,209.96
d. $2,326.27
e. $2,442.59
Page 176 M/C Problems Chapter 5: Time Value of Money
148. Your bank offers to lend you $100,000 at an 8.5% annual interest rate
to start your new business. The terms require you to amortize the loan
with 10 equal end-of-year payments. How much interest would you be
paying in Year 2?
a. $7,531
b. $7,927
c. $8,323
d. $8,740
e. $9,177
149. You are considering an investment in a Third World bank account that
pays a nominal annual rate of 18%, compounded monthly. If you invest
$5,000 at the beginning of each month, how many months would it take
for your account to grow to $250,000? Round fractional months up.
a. 23
b. 27
c. 32
d. 38
e. 44
150. You are considering investing in a bank account that pays a nominal
annual rate of 7%, compounded monthly. If you invest $3,000 at the end
of each month, how many months will it take for your account to grow to
$150,000?
a. 39.60
b. 44.00
c. 48.40
d. 53.24
e. 58.57
151. Your child’s orthodontist offers you two alternative payment plans.
The first plan requires a $4,000 immediate up-front payment. The
second plan requires you to make monthly payments of $137.41, payable
at the end of each month for 3 years. What nominal annual interest
rate is built into the monthly payment plan?
a. 12.31%
b. 12.96%
c. 13.64%
d. 14.36%
e. 15.08%
Chapter 5: Time Value of Money M/C Problems Page 177
152. Your subscription to Investing Wisely Weekly is about to expire. You
plan to subscribe to the magazine for the rest of your life, and you
can renew it by paying $85 annually, beginning immediately, or you can
get a lifetime subscription for $850, also payable immediately.
Assuming that you can earn 6.0% on your funds and that the annual
renewal rate will remain constant, how many years must you live to make
the lifetime subscription the better buy?
a. 7.48
b. 8.80
c. 10.35
d. 12.18
e. 14.33
153. You just deposited $2,500 in a bank account that pays a 4.0% nominal
interest rate, compounded quarterly. If you also add another $5,000 to
the account one year (4 quarters) from now and another $7,500 to the
account two years (8 quarters) from now, how much will be in the
account three years (12 quarters) from now?
a. $15,234.08
b. $16,035.87
c. $16,837.67
d. $17,679.55
e. $18,563.53
154. Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%,
simple interest, with interest paid quarterly. Merchants Bank offers
to lend you the $50,000, but it will charge 6.0%, simple interest, with
interest paid at the end of the year. What's the difference in the
effective annual rates charged by the two banks?
a. 1.56%
b. 1.30%
c. 1.09%
d. 0.91%
e. 0.72%
155. Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5
equal installments at the end of each of the next 5 years. By how much
would you reduce the amount you owe in the first year?
a. $2,404.91
b. $2,531.49
c. $2,658.06
d. $2,790.96
e. $2,930.51
Page 178 M/C Problems Chapter 5: Time Value of Money
156. Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5
equal installments at the end of each of the next 5 years. How much
would you still owe at the end of the first year, after you have made
the first payment?
a. $10,155.68
b. $10,690.19
c. $11,252.83
d. $11,845.09
e. $12,468.51
157. Your sister turned 35 today, and she is planning to save $7,000 per
year for retirement, with the first deposit to be made one year from
today. She will invest in a mutual fund that's expected to provide a
return of 7.5% per year. She plans to retire 30 years from today, when
she turns 65, and she expects to live for 25 years after retirement, to
age 90. Under these assumptions, how much can she spend each year
after she retires? Her first withdrawal will be made at the end of her
first retirement year.
a. $58,601
b. $61,686
c. $64,932
d. $68,179
e. $71,588
158. You agree to make 24 deposits of $500 at the beginning of each month
into a bank account. At the end of the 24th month, you will have
$13,000 in your account. If the bank compounds interest monthly, what
nominal annual interest rate will you be earning?
a. 7.62%
b. 8.00%
c. 8.40%
d. 8.82%
e. 9.26%
159. Your company has just taken out a 1-year installment loan for $72,500
at a nominal rate of 11.0% but with equal end-of-month payments. What
percentage of the 2nd monthly payment will go toward the repayment of
principal?
a. 73.67%
b. 77.55%
c. 81.63%
d. 85.93%
e. 90.45%
Chapter 5: Time Value of Money M/C Problems Page 179
160. On January 1, 2010, your brother's business obtained a 30-year
amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%,
with 360 end-of-month payments. The firm can deduct the interest paid
for tax purposes. What will the interest tax deduction be for 2010?
a. $17,419.55
b. $17,593.75
c. $17,769.68
d. $17,947.38
e. $18,126.85
161. Steve and Ed are cousins who were both born on the same day, and both
turned 25 today. Their grandfather began putting $2,500 per year into
a trust fund for Steve on his 20th birthday, and he just made a 6th
payment into the fund. The grandfather (or his estate's trustee) will
make 40 more $2,500 payments until a 46th and final payment is made on
Steve's 65th birthday. The grandfather set things up this way because
he wants Steve to work, not be a “trust fund baby,” but he also wants
to ensure that Steve is provided for in his old age.
Until now, the grandfather has been disappointed with Ed, hence
has not given him anything. However, they recently reconciled, and the
grandfather decided to make an equivalent provision for Ed. He will
make the first payment to a trust for Ed today, and he has instructed
his trustee to make 40 additional equal annual payments until Ed turns
65, when the 41st and final payment will be made. If both trusts earn
an annual return of 8%, how much must the grandfather put into Ed's
trust today and each subsequent year to enable him to have the same
retirement nest egg as Steve after the last payment is made on their
65th birthday?
a. $3,726
b. $3,912
c. $4,107
d. $4,313
e. $4,528
162. After graduation, you plan to work for Dynamo Corporation for 12 years
and then start your own business. You expect to save and deposit
$7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000
annually for the following 6 years (t = 7 through t = 12). The first
deposit will be made a year from today. In addition, your grandfather
just gave you a $25,000 graduation gift which you will deposit
immediately (t = 0). If the account earns 9% compounded annually, how
much will you have when you start your business 12 years from now?
a. $238,176
b. $250,712
c. $263,907
d. $277,797
e. $291,687
Page 180 M/C Problems Chapter 5: Time Value of Money
163. You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To
repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the
end of Year 2, and $7,500 at the end of Year 3, plus a fixed but
currently unspecified cash flow, X, at the end of each year from Year 4
through Year 7. Breck is essentially riskless, so you are confident
the payments will be made. You regard 8% as an appropriate rate of
return on a low risk but illiquid 7-year loan. What cash flow must the
investment provide at the end of each of the final 4 years, that is,
what is X?
a. $4,271.67
b. $4,496.49
c. $4,733.15
d. $4,969.81
e. $5,218.30
164. John and Daphne are saving for their daughter Ellen's college
education. Ellen just turned 10 (at t = 0), and she will be entering
college 8 years from now (at t = 8). College tuition and expenses at
State U. are currently $14,500 a year, but they are expected to
increase at a rate of 3.5% a year. Ellen should graduate in 4 years--
if she takes longer or wants to go to graduate school, she will be on
her own. Tuition and other costs will be due at the beginning of each
school year (at t = 8, 9, 10, and 11).
So far, John and Daphne have accumulated $15,000 in their college
savings account (at t = 0). Their long-run financial plan is to add an
additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4).
Then they plan to make 3 equal annual contributions in each of the
following years, t = 5, 6, and 7. They expect their investment account
to earn 9%. How large must the annual payments at t = 5, 6, and 7 be
to cover Ellen's anticipated college costs?
a. $1,965.21
b. $2,068.64
c. $2,177.51
d. $2,292.12
e. $2,412.76
CHAPTER 5
ANSWERS AND SOLUTIONS
Page 182 Answers Chapter 5: Time Value of Money
