Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
Chapter 5: Time Value of Money
Multiple Choice Questions
1. Section: 5.2 Simple Interest; 5.3 Compound Interest
Learning Objective: 5.2; 5.3
2. Section: 5.2 Simple Interest; 5.3 Compound Interest
Learning Objective: 5.2; 5.3
3. Section: 5.2 Simple Interest; 5.3 Compound Interest
4. Section: 5.2 Simple Interest; 5.3 Compound Interest
Learning Objective: 5.2; 5.3
Level of difficulty: Basic
5. Section: 5.3 Compound Interest
Learning Objective: 5.3
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
6. Section: 5.2 Simple Interest; 5.3 Compound Interest
Learning Objective: 5.2; 5.3
Level of difficulty: Intermediate
7. Section: 5.3 Compound Interest
Learning Objective: 5.3
Level of difficulty: Intermediate
8. Section: 5.3 Compound Interest
Learning Objective: 5.3
Level of difficulty: Intermediate
9. Section: 5.4 Annuities and Perpetuities
Learning objective: 5.4
Level of difficulty: Intermediate
10. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Challenging
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
11. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Intermediate
12. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Basic
13. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Basic
14. Section: 5.7 Loan or Mortgage Arrangements
Learning Objective: 5.7
Level of difficulty: Intermediate
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
15. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Challenging
Practice Problems
Basic
16. Section: 5.2 Simple Interest
Learning Objective: 5.2
Level of difficulty: Basic
Solution:
As this is simple interest, Dmitri will earn the same amount of interest each year. The annual
17. Section: 5.2 Simple Interest
Learning Objective: 5.2
Level of difficulty: Basic
Solution:
18. Section: 5.2 Simple Interest
Learning Objective: 5.2
Level of difficulty: Basic
Solution:
As the exact amount of interest owing each year will be paid, there is no “compounding.” The
19. Section: 5.2 Simple Interest
Learning Objective: 5.2
Level of difficulty: Basic
Solution:
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
20. Section: 5.3 Compound Interest
Learning Objective: 5.3
Level of difficulty: Basic
Solution:
The payment of compound interest means that we must compound (or find the future value of)
21. Section: 5.2 Simple Interest; 5.3 Compound Interest
Learning outcome: 5.2; 5.3
Level of difficulty: Basic
Solution:
22. Section: 5.3 Compound Interest
Learning outcome: 5.3
Level of difficulty: Basic
Solution:
The future value of the loan (the amount to be repaid) is $5,000. The amount that can be
23. Section: 5.3 Compound Interest
Learning Objective: 5.3
Level of difficulty: Basic
Solution:
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
24. Section: 5.3 Compound Interest
Learning Objectives: 5.3
Level of difficulty: Basic
Solution:
Jon needs $800 in three years; that is the future value amount. The present value equivalent is:
25. Section: 5.4 Annuities and Perpetuities
Learning outcome: 5.4
Level of difficulty: Basic
Solution:
Present value of the perpetual scholarship payment:
26. Section: 5.6 Quoted versus Effective Rates
Learning Objective: 5.6
Level of difficulty: Basic
Solution:
27. Section: 5.6 Quoted versus Effective Rates
Learning Objective: 5.6
Level of difficulty: Basic
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
Solution:
a. For annual compounding, the effective annual rate will be the same as the quoted rate. To
check this:
28. Section: 5.6 Quoted versus Effective Rates
Learning Objective: 5.6
Level of difficulty: Basic
Solution:
29. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Basic
Solution:
The value of any perpetual stream of payments can be valued as a perpetuity:
30. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Basic
Solution:
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
Because the fees are paid at the start of the year, this is an annuity due.
31. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Basic
Solution:
The future value amount is $40,000. The amount to be saved each year is really the payment on
32. Section: 5.5 Growing Annuities and Perpetuities
Learning Objective: 5.5
Level of difficulty: Basic
Solution:
33. Section: 5.8 Comprehensive Examples
Learning Objective: 5.7
Level of difficulty: Basic
Solution:
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
34. Section: 5.8 Comprehensive Examples
Learning Objective: 5.8
Level of difficulty: Basic
Solution:
This is an ordinary annuity.
Intermediate
35. Section: 5.1 Opportunity Cost
Learning Objective: 5.1
Level of difficulty: Intermediate
Solution:
36. Section: 5.4 Annuities and Perpetuities
Learning outcome: 5.4
Level of difficulty: Intermediate
Solution:
Present value of the perpetual scholarship payment at the end of 4 years:
37. Section: 5.4 Annuities and Perpetuities
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
Learning outcome: 5.4
Level of difficulty: Intermediate
Solution:
Find the present value of the four-year annuity at year 3:
38. Section: 5.4 Annuities and Perpetuities
Learning outcome: 5.4
Level of difficulty: Intermediate
Solution:
To be indifferent between the two options means that the present value of the annuity must equal
39. Section: 5.6 Quoted versus Effective Rates
Learning Objective: 5.6
Level of difficulty: Intermediate
Solution:
Step 1: determine monthly effective rate
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
40. Section: 5.6 Quoted versus Effective Rates
Learning Objective: 5.6
Level of difficulty: Intermediate.
Solution:
41. Section: 5.4 Annuities and Perpetuities
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
Learning Objective: 5.4
Level of difficulty: Intermediate
Solution:
A. The future value of Jane’s account will be:
42. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Intermediate
Solution:
Find the present value of the four-year annuity due:
Now, discount this amount back five years:
43. Section: 5.4 Annuities and Perpetuities
Learning Objective: 5.4
Level of difficulty: Intermediate
Solution:
We have two separate annuities to consider: the tuition payments, and the savings amounts. First,
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
44. Section: 5.5 Growing Annuities and Perpetuities
Learning Objective: 5.5
Level of difficulty: Intermediate
Solution:
45. Section: 5.5 Growing Annuities and Perpetuities
Learning Objective: 5.5
Level of difficulty: Intermediate
Solution:
46. Section: 5.5 Growing Annuities and Perpetuities
Learning Objective: 5.5
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
Level of difficulty: Intermediate
Solution:
To solve this we need to realize that the present value of a perpetuity (growing or otherwise)
47. Section: 5.4 Annuities and Perpetuities 5.6; Quoted versus Effective Rates
Learning Objective: 5.4; 5.6
Level of difficulty: Intermediate
Solution:
Solve the annuity equation to find k, the interest rate:
48. Section: 5.4 Annuities and Perpetuities; 5.6 Quoted versus Effective Rates
Learning Objective: 5.4; 5.6
Level of difficulty: Intermediate
Solution:
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
49. Section: 5.6 Quoted versus Effective Rates
Learning Objective: 5.6
Level of difficulty: Intermediate
Solution:
50. Section: 5.7 Loan or Mortgage Arrangements
Learning Objective: 5.7
Level of difficulty: Intermediate
Solution:
a. In Canada, fixed-rate mortgages use semi-annual compounding of interest, so m=2. The
Introduction to Corporate Finance, Fourth Edition Booth, Cleary, Rakita
51. Section: 5.7 Loan or Mortgage Arrangements
Learning Objective: 5.7
Level of difficulty: Intermediate
Solution:
With semi-annual compounding (the norm in Canada) and monthly payments, m=2 and f=12.The
52. Section: 5.8 Comprehensive Examples
Learning Objective: 5.8
Level of difficulty: Intermediate
Solution:
a. This is an annuity due. Timmy makes his first payment on his 21st birthday and the last