Chapter 05: Time Value of Money
142. Suppose you deposited $27,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year.
How much would be in the account after 8 months, assuming each month has 30 days?
a.
$34,952.08
b.
$30,478.21
c.
$27,961.66
d.
$30,198.59
e.
$29,918.98
c
b.
c.
d.
e.
MODERATE
5-17 Fractional Time Periods
Chapter 05: Time Value of Money
143. Suppose you borrowed $27,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the
next 4 years. How large would your payments be?
a.
$10,000.86
b.
$8,334.05
c.
$6,500.56
d.
$10,250.89
e.
$6,333.88
b.
c.
d.
e.
MODERATE
5-18 Amortized Loans
144. Suppose you are buying your first condo for $300,000, 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.
$1,459.13
b.
$1,369.06
c.
$2,179.69
d.
$2,215.71
Chapter 05: Time Value of Money
e.
$1,801.39
e
b.
c.
d.
e.
MODERATE
5-18 Amortized Loans
145. Your uncle will sell you his bicycle shop for $280,000, 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.
$4,747.31
b.
$5,651.56
c.
$5,425.49
d.
$5,934.13
e.
$4,408.21
b.
c.
d.
e.
5-18 Amortized Loans
Chapter 05: Time Value of Money
146. Suppose you borrowed $15,000 at a rate of 11.8% 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.
$1,362.90
b.
$1,557.60
c.
$1,716.90
d.
$1,770.00
e.
$1,893.90
MODERATE
5-18 Amortized Loans
147. You plan to borrow $45,200 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.
$2,403.37
Chapter 05: Time Value of Money
b.
$2,703.80
c.
$2,854.01
d.
$3,004.22
e.
$3,454.85
MODERATE
5-18 Amortized Loans
148. Your bank offers to lend you $113,200 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.
$7,178.72
b.
$8,076.06
c.
$8,524.73
d.
$8,973.40
e.
$10,319.41
Chapter 05: Time Value of Money
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 $280,000? Round fractional months up.
a.
39
b.
41
c.
43
d.
50
e.
36
Chapter 05: Time Value of Money
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 $200,000?
a.
65.52
b.
52.53
c.
66.65
d.
56.48
e.
61.00
b.
c.
d.
e.
MODERATE
Comprehensive
b.
c.
d.
e.
MODERATE
Comprehensive
Chapter 05: Time Value of Money
151. Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $3,500 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.
27.18%
b.
23.81%
c.
24.05%
d.
21.41%
e.
19.24%
c
c.
e.
MODERATE
Comprehensive
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
$740, 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.
10.48
Chapter 05: Time Value of Money
b.
10.72
c.
11.65
d.
9.32
e.
11.42
c
b.
c.
d.
e.
CHALLENGING
5-10 Finding Annuity Payments, Periods, and Interest Rates
153. 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 $13,150 in your account. If the bank compounds interest monthly, what nominal annual interest rate
will you be earning?
a.
9.83%
b.
8.00%
c.
9.13%
d.
6.87%
e.
8.70%
e
b.
Chapter 05: Time Value of Money
154. You just deposited $6,500 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.
$20,543.18
b.
$15,407.38
c.
$17,461.70
d.
$20,748.61
e.
$24,857.24
a
b.
c.
d.
e.
CHALLENGING
5-15 Semiannual and Other Compounding Periods
c.
d.
e.
CHALLENGING
5-10 Finding Annuity Payments, Periods, and Interest Rates
Chapter 05: Time Value of Money
155. 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 6.2%, 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.
1.33%
b.
1.09%
c.
0.91%
d.
1.11%
e.
0.83%
b.
c.
d.
e.
CHALLENGING
5-16 Comparing Interest Rates
156. Suppose you borrowed $75,000 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.
$17,414.67
b.
$16,892.23
c.
$19,852.73
d.
$18,807.85
e.
$18,633.70
a
Chapter 05: Time Value of Money
157. Suppose you borrowed $30,000 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.
$19,118.33
b.
$22,112.76
c.
$22,343.11
d.
$23,034.13
e.
$20,961.06
b.
c.
d.
e.
CHALLENGING
5-18 Amortized Loans
b.
c.
d.
e.
CHALLENGING
5-18 Amortized Loans
Chapter 05: Time Value of Money
158. Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.5% but with equal
end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?
a.
90.94%
b.
72.03%
c.
73.83%
d.
90.04%
e.
96.34%
b.
c.
d.
e.
CHALLENGING
5-18 Amortized Loans
Amortization
159. Your brother’s business obtained a 30-year amortized mortgage loan for $125,000 at a nominal annual rate of 7.0%,
Chapter 05: Time Value of Money
with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax
deduction be for Year 1?
a.
$10,800.12
b.
$7,229.11
c.
$8,709.78
d.
$8,100.09
e.
$8,012.99
c
b.
c.
d.
e.
CHALLENGING
5-18 Amortized Loans
160. Your sister turned 35 today, and she is planning to save $85,000 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
Chapter 05: Time Value of Money
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.
$898,847.29
b.
$749,039.41
c.
$756,924.04
d.
$788,462.54
e.
$607,116.15
b.
c.
d.
e.
CHALLENGING
Comprehensive
161. Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began
putting $2,300 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 $2,300 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.
$2,639
b.
$2,673
c.
$3,359
d.
$3,428
Chapter 05: Time Value of Money
e.
$3,565
CHALLENGING
Comprehensive
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
$32,500 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.
$236,125
b.
$319,814
c.
$298,892
d.
$295,903
e.
$289,925
c
Chapter 05: Time Value of Money
163. You are negotiating to make a 7-year loan of $37,500 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.
$9,487.32
b.
$11,479.65
c.
$8,918.08
d.
$11,384.78
e.
$10,246.30
a
b.
c.
d.
e.
CHALLENGING
Comprehensive
Chapter 05: Time Value of Money
b.
c.
d.
e.
CHALLENGING
Comprehensive
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 $18,000 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.
$562.25
b.
$658.42
c.
$739.80
d.
$917.35
e.
$673.22
Chapter 05: Time Value of Money
Chapter 05: Time Value of Money