978-0133546408 Chapter 5 Solution Manual Part 3

Chapter 5: Time Value of Money 73

P5-37. Compounding frequency, time value, and effective annual rates

LG 5; Intermediate

a. Compounding frequency:

AN  10, I  3%, PV  $2,500 BN  18, I  2%, PV  $50,000

CN  10, I  5%, PV  $1,000 DN  24, I  4%, PV  $20,000

b. Effective interest rate: ieff  (1  r%/m)m – 1

Aieff  (1  0.06/2)2  1 Bieff  (1  0.12/6)6  1

Cieff  (1  0.05/1)1  1 Dieff  (1  0.16/4)4 – 1

c. The effective rates of interest rise relative to the stated nominal rate with increasing compounding

frequency.

P5-38. Continuous compounding: FVcont.  PVex (e  2.7183)

LG 5; Intermediate

P5-39. Personal finance: Compounding frequency and time value

LG 5; Challenge

a. (1) N  10; I  8%, PV  $2,000 (2) N  20, I  4%, PV  $2,000

(3) N  3650; I  8  365  0.022, PV  $2,000 (4) FV10  $2,000(e0.8)

b. (1) ieff  (1  0.08/1)1  1 (2) ieff  (1  0.08/2)2  1

(3) ieff  (1  0.08/365)365  1 (4) ieff  (ek 1)

74 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

d. The more frequent the compounding the larger the future value. This result is shown in part a by the

P5-40. Personal finance: Comparing compounding periods

LG 5; Challenge

a. (1) Annually: N  2, I  12%, PV  $15,000

(2) Quarterly: N  2  4  8; I  12  4  3%, PV  $15,000

(3) Monthly: N  2  12  24; I  12  12  1%; PV  $15,000

(4) Continuously: FVcont.  PVerx t

b. The future value of the deposit increases from $18,816 with annual compounding to $19,068.77 with

c. The maximum future value for this deposit is $19,068.77, resulting from continuous compounding, which

P5-41. Personal finance: Annuities and compounding

LG 3, 5; Intermediate

a.

(1) Annual

(2) Semiannual

(3) Quarterly

b. The sooner a deposit is made, the sooner the funds will be available to earn interest and contribute to

P5-42. Deposits to accumulate growing future sum

LG 6; Basic

Case Terms Calculation Payment

Chapter 5: Time Value of Money 75

P5-43. Personal finance: Creating a retirement fund

LG 6; Intermediate

a. N  42, I  8%, FV  $220,000 b. N  42, I 8%, PMT  $600

P5-44. Personal finance: Accumulating a growing future sum

LG 6: Intermediate

Step 1: Determining the cost of a home in 20 years.

Step 2: Determining how much has to be saved annually to afford a home.

P5-45. Personal finance: Deposits to create a perpetuity

LG 3, 6; Intermediate

a. Present value of a perpetuity  PMT r

P5-46. Personal finance: Inflation, time value, and annual deposits

LG 2, 3, 6; Challenge

a. N  25, I  5%, PV $200,000

b. N  25, I  9%, FV  $677,270.99

c. Because John will have an additional year on which to earn interest at the end of the 25 years, his

annuity due deposit will be smaller each year. To determine the annuity amount, John will first

discount back the $677,200 one period.

P5-47. Loan payment

LG 6; Basic

Loan

76 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

CN  30, I  10%, PV  $75,000 DN  5, I  15%, PV  $4,000

P5-48. Personal finance: Loan amortization schedule

LG 6; Intermediate

a. N  3, I  14%, PV  $15,000

b.

End of

Year

Loan

Payment

Beginning-of-

Year Principal

Payments End-of-Year

Principal

Interest Principal

c. Through annual end-of-the-year payments, the principal balance of the loan is declining, causing less

P5-49. Loan interest deductions

LG 6; Challenge

a. N  3, I  13%, PV  $10,000

b.

End of

Year

Loan

Payment

Beginning-of-

Year Principal

Payments End-of-Year

Principal

Interest Principal

P5-50. Personal finance: Monthly loan payments

LG 6; Challenge

a. N  12  2  24, I  12%/12  1%, PV  $4,000 ($4,500  500)

b. N  12  2  24, I  9%/12  0.75%, PV  $4,000

P5-51. Growth rates

LG 6; Basic

a. Case

AN  4, PV  $500, FV  $800.BN  9, PV  $1,500, FV  $2,280

CN  6, PV  $2,500, FV  $2,900

b. Case

Chapter 5: Time Value of Money 77

P5-52. Personal finance: Rate of return

LG 6, Intermediate

a. N  3, PV  $1,500, FV  $2,000

P5-53. Personal finance: Rate of return and investment choice

LG 6; Intermediate

a. AN  6, PV  5,000, FV  $8,400 BN  15, PV  $5,000, FV  $15,900

CN  4, PV  $5,000, FV  $7,600 DN  10, PV  $5,000, FV $13,000

b. Investment C provides the highest return of the four alternatives. Assuming equal risk for the

P5-54. Rate of return-annuity

LG 6; Basic

P5-55. Personal finance: Choosing the best annuity

LG 6; Intermediate

a. Annuity A Annuity B

b. Annuity B gives the highest rate of return at 9% and would be the one selected based upon Raina’s

criteria.

P5-56. Personal finance: Interest rate for an annuity

LG 6; Challenge

a. Defendants interest rate assumption

b. Prosecution interest rate assumption

78 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

c. N  25, I  9%, PV  $2,000,000

P5-57. Personal finance: Loan rates of interest: PVAn  PMT(PVIFAi%,n)

LG 6; Intermediate

a. Loan A Loan B

Loan C

b. Mr. Fleming should choose Loan B, which has the lowest interest rate.

P5-58. Number of years to equal future amount

LG 6; Intermediate

AI  7%, PV  $300, FV  $1,000 BI  5%, PV  $12,000, FV  $15,000

CI  10%, PV  $9,000, FV  $20,000 DI  9%, PV  $100, FV  $500

EI  15%, PV  $7,500, FV  $30,000

P5-59. Personal finance: Time to accumulate a given sum

LG 6; Intermediate

a. I  10%, PV  $10,000, FV  $20,000

b. I  7%, PV  $10,000, FV  $20,000

c. I  12%, PV  $10,000, FV  $20,000

P5-60. Number of years to provide a given return

LG 6; Intermediate

AI  11%, PV  $1,000, PMT  $250 BI  15%, PV  $150,000, PMT  $30,000

CI  10%, PV  $80,000, PMT  $10,000 DI  9%, PV  $600, PMT  275

EI  6%, PV  $17,000, PMT  $3,500

P5-61. Personal finance: Time to repay installment loan

LG 6; Intermediate

a. I  12%, PV  $14,000, PMT  $2,450

b. I  9%, PV  $14,000, PMT  $2,450

Chapter 5: Time Value of Money 79

c. I  15%, PV  $14,000, PMT  $2,450

P5-62. Ethics problem

LG 6; Intermediate

This is a tough issue. Even back in the Middle Ages, scholars debated the idea of a “just price.” The

ethical debate hinges on (1) the basis for usury laws, (2) whether full disclosure is made of the true cost of

the advance, and (3) whether customers understand the disclosures. Usury laws are premised on the notion

 Case

Case studies are available on www.myfinancelab.com.

Finding Jill Moran’s Retirement Annuity

Chapter 5’s case challenges the student to apply present value and future value techniques to a real-world situation.

The first step in solving this case is to determine the total amount Sunrise Industries needs to accumulate until Ms.

Moran retires, remembering to take into account the interest that will be earned during the 20-year payout period. Once

that is calculated, the annual amount to be deposited can be determined.

a.

b. Total amount to accumulate by end of year 12

c. End-of-year deposits at 9% interest

d. End-of-year deposits, 10% interest

80 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition

e. Initial deposit if annuity is a perpetuity and initial deposit earns 9%:

PVperp  PMT r

 Spreadsheet Exercise

The answer to Chapter 5’s Uma Corporation spreadsheet problem is located on the Instructor’s Resource Center at

www.pearsonhighered.com/irc under the Instructor’s Manual.

 Group Exercise

Group exercises are available on www.myfinancelab.com.

This set of deliverables concerns each group’s fictitious firm. The first scenario involves the replacement of a copy

machine. The first decision pertains to a choice between competing leases, while the second is choosing among

For the savings plan the groups are asked to look at several deposit options, while for the computer upgrade purchase

an amortization schedule must be developed. Modifications or even elimination of one of these scenarios is