CHAPTER 28—TIME VALUE OF MONEY
152. 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
153. The store where you bought new home furnishings 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 28—TIME VALUE OF MONEY
154. Your Green Investment Tips subscription 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
e
155. 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.
$16,035.88
c.
$16,837.67
d.
$17,679.55
e.
$18,563.53
CHAPTER 28—TIME VALUE OF MONEY
156. Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. An
offer to lend you the $50,000 also comes from Community Bank, 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%
CHAPTER 28—TIME VALUE OF MONEY
157. 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
158. 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
e
CHAPTER 28—TIME VALUE OF MONEY
159. Your older brother turned 35 today, and he is planning to save $7,000 per year for retirement, with the first deposit to
be made one year from today. He will invest in a mutual fund that’s expected to provide a return of 7.5% per year. He
plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under
these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his
first retirement year.
a.
$58,601
b.
$61,686
c.
$64,932
d.
$68,179
e.
$71,588
c
Difficulty: Challenging
INTE.GENE.16.203 – LO: 28–10
United States – BUSPROG: Analytic
United States – AK – DISC: Time value of money
United States – OH – Default City – TBA
Retirement planning
TYPE: Multiple Choice: Problem
160. 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%
a
United States – BUSPROG: Analytic
United States – AK – DISC: Time value of money
United States – OH – Default City – TBA
Amortization: ending bal.
TYPE: Multiple Choice: Problem
CHAPTER 28—TIME VALUE OF MONEY
161. Your business 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%
e
Amortization
CHAPTER 28—TIME VALUE OF MONEY
162. On January 1, 2016, your sister’s pet supplies 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 2016?
a.
$17,419.55
b.
$17,593.75
c.
$17,769.68
d.
$17,947.38
e.
$18,126.85
a
163. You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9
more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect
to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be
to enable you to reach your $50,000 target?
a.
$3,008
b.
$3,342
CHAPTER 28—TIME VALUE OF MONEY
c.
$3,676
d.
$4,044
e.
$4,448
CHAPTER 28—TIME VALUE OF MONEY
164. Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is
invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the
nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate
as inflation and thus enabling her to maintain a constant standard of living?
a.
$65,632
b.
$72,925
c.
$81,027
d.
$89,130
e.
$98,043
c
CHAPTER 28—TIME VALUE OF MONEY
CHAPTER 28—TIME VALUE OF MONEY
165. Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather
began putting $2,500 per year into a trust fund for Julian 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 Julian’s 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a “trust fund
baby,” but he also wants to ensure that Julian is provided for in his old age.
Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they
recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first
payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until
Jonathan 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 Jonathan‘s trust today and each subsequent year to enable him to have the same retirement
nest egg as Julian 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
a
CHAPTER 28—TIME VALUE OF MONEY
166. You plan to work for Strickland Corporation for 12 years after graduation and after that want to 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
grandmother just gave you a $25,000 graduation gift that 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
167. You are in negotiations to make a 7-year loan of $25,000 to DeVille Corporation. To repay you, DeVille 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. You are confident the payments will be
made, since DeVille is essentially riskless. 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
c
CHAPTER 28—TIME VALUE OF MONEY
168. Scott and Linda have been saving to pay for their daughter Casie’s college education. Casie 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, Scott and Linda 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 Casie’s anticipated college costs?
a.
$1,965.21
b.
$2,068.64
c.
$2,177.51
d.
$2,292.12
e.
$2,412.76
e
CHAPTER 28—TIME VALUE OF MONEY
CHAPTER 28—TIME VALUE OF MONEY