Deck 4: Time Value of Money

Question 1

Which of the following types of annuities best describes a mortgage payment or payment of rent that normally must be paid at the beginning of each month?

A)Annuity due
B)Ordinary annuity
C)Deferred annuity
D)Annuity in arrears
E)Immediate annuity

Answer 1

  A

Question 2

Which of the following is the correct expression for calculating the future value of an investment? (r represents the interest rate and n represents the length of time)

A)Future value = Present value × (1 + r)ⁿ
B)Future value = Present value + (1 + r)ⁿ
C)Future value = Present value - (1 + r)ⁿ
D)Future value = Present value / (1 + r)ⁿ
E)Future value = Present value / [(1 + r) × n]

Answer 2

Future value = Present value × (1 + r)ⁿ

Question 3

In most instances, the payment of utility bills is an example of _____. 

A)immediate annuity
B)ordinary annuity
C)annuity due
D)lump-sum payments
E)uneven cash flows

Answer 3

  E

Question 4

Robert plans to invest $650 in a savings account at the beginning of each of the next seven years. If his opportunity cost rate is 5 percent compounded annually, how much will his investment be worth at the end of seven years?

A)$5,048
B)$5,292
C)$5,557
D)$6,058
E)$6,656

Question 5

Adam plans to invest $1500 today in a mutual fund. If he earns 12 percent interest compounded monthly, to what amount will his investment grow in 20 years?

A)$17,289
B)$15,897
C)$16,339
D)$12,450
E)$18,546

Question 6

Pelican Corporation is planning to invest $12,000 at the beginning of each of the next eight years. This form of cash flow pattern is known as a(n) _____. 

A)immediate annuity
B)annuity due
C)uneven cash flow stream
D)ordinary annuity
E)deferred annuity

Question 7

Which of the following is the rate of return on the best available alternative investment of equal risk?

A)Amortization rate
B)Risk adjusted rate
C)Required rate of return
D)Opportunity cost rate
E)Expected rate of return

Question 8

At the beginning of the year, William bought 20 shares of Zync Corporation at $18.50 per share. Zync pays dividend at the end of each year based on annual profits, which generally vary substantially from year to year. In its 25 years history, Zync has paid dividends every year without fail. The initial investment by William and the receipt of dividend at the end of every year are examples of a(n) _____ and a(n) _____, respectively. 

A)uneven cash flow stream; annuity due
B)uneven cash flow stream; ordinary annuity
C)lump-sum payment; annuity due
D)lump-sum payment; uneven cash flow stream
E)lump-sum payment; ordinary annuity

Question 9

A firm plans to make investments of $5,000 for the next 10 years, paying the amount at the end of each year. This form of cash flow pattern represents a(n) _____. 

A)lump-sum payment
B)uneven cash flow stream
C)annuity due
D)ordinary annuity
E)immediate annuity

Question 10

Ibiza Corporation invested $20,000 for the last four years in an investment that will pay the firm $120,000 at the end of this year. The $120,000 received at the end of this year is an example of a(n) _____. 

A)uneven cash flow
B)annuity due
C)ordinary annuity
D)deferred annuity
E)lump-sum amount

Question 11

The process of determining the value to which an amount or a series of cash flows will grow in the future when interest on interest is applied is known as _____. 

A)discounting
B)compounding
C)amortization
D)consolidation
E)annualizing

Question 12

An investor purchased a 10-year bond that makes a $50 interest payment at the end of every six-month period until the bond matures. These interest payments represent a(an) _____. 

A)perpetuity
B)ordinary annuity
C)annuity due
D)compounded annuity
E)discounted annuity

Question 13

An annuity with payments that occur at the beginning of each period is known as a _____. 

A)deferred annuity
B)ordinary annuity
C)immediate annuity
D)annuity due
E)discounted annuity

Question 14

A firm makes investments of $2,000 this year, $4,000 next year, and $2,500 the following year. This form of cash flow pattern is a(n) _____. 

A)ordinary annuity
B)annuity due
C)uneven cash flow stream
D)lump-sum payment
E)compounded cash flow

Question 15

Ten years ago, Emma purchased an investment for $22,500. The investment earned 7 percent interest each year. What is the value of the investment today?

A)$36,667.76
B)$38,250.26
C)$40,527.37
D)$44,260.91
E)$46,458.63

Question 16

When the payment for an annuity is made at the end of each period, such an annuity is referred to as a(n) _____. 

A)ordinary annuity
B)annuity due
C)immediate annuity
D)terminal annuity
E)discounted annuity

Question 17

Dwayne plans to invest $4,700 in a savings account at the beginning of each of the next 12 years. If his opportunity cost rate is 7 percent compounded annually, how much will his investment be worth at the end of 12 years?

A)$87,542.29
B)$89,961.02
C)$91,250.52
D)$93,668.27
E)$84,075.72

Question 18

Shekhar plans to invest $1,820 in a mutual fund at the end of each of the next six years. If his opportunity cost rate is 8 percent compounded annually, how much will his investment be worth after the last annuity payment is made? Use the equation method to calculate the worth of the investment. 

A)$11,125.76
B)$11,857.58
C)$12,580.20
D)$13,351.39
E)$14,871.32

Question 19

Sarah invests $2,700 today in an account that pays 6 percent interest compounded annually. She wants to know the total balance in her account five years from today. Identify the correct keystrokes to be used in a financial calculator to determine the total balance. 

A)N = 6, I/Y = 5%, PV = 2,700
B)N = 5, I/Y = 6%, FV = -2,700
C)N = 5, I/Y = 6%, PV = 2,700
D)N = 5, I/Y = 6%, FV = 2,700
E)N = 5, I/Y = 6%, PV = -2,700

Question 20

Shaun is planning to invest $570 in a mutual fund at the end of each of the next eight years. If his opportunity cost rate is 6 percent compounded annually, how much will his investment be worth after the last annuity payment is made?

A)$5,055
B)$5,642
C)$5,980
D)$6,026
E)$6,222

Question 21

Dire invested $10,000 today in an investment that has a maturity value of $13,500 in five years. If the interest is compounded annually, what is the annual rate of return earned on the investment?

A)7.8%
B)8.2%
C)6.2%
D)4.5%
E)9.5%

Question 22

Andrea's opportunity cost rate is 12 percent compounded annually. How much must she deposit in an account today if she wants to receive $2,100 at the beginning of each of the next seven years? Use the equation method to determine the amount. 

A)$10,734
B)$11,625
C)$10,998
D)$11,887
E)$9,584

Question 23

Jude wants to receive $1,100 at the beginning of each of the next eight years. If his opportunity cost rate is 9 percent compounded annually, how much must he deposit in an account today? Use a financial calculator to make the calculation. 

A)$6,088
B)$7,086
C)$6,874
D)$6,636
E)$6,420

Question 24

Bill is considering investing $450 at the end of every month in a fixed income instrument. He will receive $27,000 at the end of four years. If interest is compounded monthly, what is the effective annual rate of return earned on the investment?

A)11.6%
B)22.3%
C)15.1%
D)11.1%
E)13.6%

Question 25

The future value of an uneven cash flow stream is also referred to as its _____. 

A)discounted value
B)amortized value
C)consolidated value
D)terminal value
E)periodic value

Question 26

The process of determining the present value of a cash flow or a series of cash flows to be received or paid in the future is known as _____. 

A)compounding
B)discounting
C)consolidation
D)amortization
E)annualizing

Question 27

Lisa's opportunity cost rate is 10 percent compounded annually. How much must she deposit in an account today if she wants to receive $3,200 at the end of each of the next 12 years? Use the equation method to determine the amount to be deposited today. 

A)$17,226
B)$14,868
C)$23,252
D)$18,725
E)$21,804

Question 28

If the opportunity cost rate is 8 percent, compounded annually, what is the present value of $8,200 due to be received in 12 years?

A)$3,068
B)$3,256
C)$3,552
D)$3,688
E)$3,854

Question 29

Identify the correct equation for calculating the present value of an investment. (Assume 'r' stands for rate of return and 'n' stands for number of periods interest is earned.)

A)Present value = Future value × (1 + r)ⁿ
B)Present value = Future value + (1 + r)ⁿ
C)Present value = Future value - (1 + r)ⁿ
D)Present value = Future value / (1 + r)ⁿ
E)Present value = Future value / ((1 + r) × n)

Question 30

Jason's opportunity cost rate is 8 percent compounded annually. How much must he deposit in an account today if he wants to receive $5,400 at the end of each of the next 10 years?

A)$32,625
B)$34,852
C)$36,234
D)$38,996
E)$40,252

Question 31

Joey is planning to invest his savings in a fixed income fund. He manages to deposit $700 at the end of the first year, $500 at the end of the second year, $300 at the end of the third year, and $600 at the end of the fourth year. If the fund earns 6 percent interest each year, the terminal (future) value of this uneven cash flow stream at the end of Year 4 is _____. 

A)$2,314
B)$1,833
C)$2,097
D)$2,355
E)$1,784

Question 32

Mike is considering investing $18,500 in an investment that will have a maturity value of $32,500 in eight years. If the interest is compounded monthly, what is the effective annual rate of return earned on the investment?

A)4.3%
B)5.7%
C)6.5%
D)7.3%
E)8.8%

Question 33

Liam is considering putting money in an investment plan that will pay him $52,000 in 12 years. If Liam's opportunity cost rate is 7 percent compounded annually, what is the maximum amount he should be willing to pay for the investment today?

A)$23,089
B)$25,526
C)$26,888
D)$28,685
E)$30,534

Question 34

Paul wants to accumulate $14,500 for the down payment for a new condo. He plans to start investing $2,500 annually beginning today. The investment account will pay 10 percent interest compounded annually. How long would it take him to accumulate enough money to make the down payment?

A)3.5 years
B)5.9 years
C)6.1 years
D)4.4 years
E)4.8 years

Question 35

LeGo Financials offer two investment plans. Investment A pays 9 percent interest compounded monthly, whereas Investment B pays 10 percent interest compounded semiannually. What are the effective annual rates of Investment A and Investment B?

A)9.38 percent and 10.50 percent, respectively
B)9.38 percent and 10.25 percent, respectively
C)9.75 percent and 10.25 percent, respectively
D)9.75 percent and 10.50 percent, respectively
E)9.94 percent and 10.45 percent, respectively

Question 36

Rebecca is currently working, but is planning to start a college in few years. For this purpose, she would need $20,000. Today she can start investing $750 monthly in an investment account that pays 6 percent compounded monthly. How long would it take her to have enough money to start college?

A)28.5 months
B)27.8 months
C)25.0 months
D)22.6 months
E)30.3 months

Question 37

Glen wants to take a holiday that costs $8,850, but currently he only has $2,750 saved. If he invests this money at 8 percent interest compounded annually, how long will he have to wait to take his holiday?

A)12.36 years
B)16.25 years
C)15.19 years
D)13.52 years
E)14.12 years

Question 38

Zoey is planning to invest $5,000 in a fixed income security at the end of each of the next four years. She will receive $23,000 at the end of four years. If interest is compounded annually, what is the annual rate of return earned on the investment?

A)5.7%
B)7.3%
C)8.7%
D)10.2%
E)9.4%

Question 39

Five years ago, Brian had invested $14,850 in a growth fund. The investment is worth $22,000 today. If the interest was compounded annually, what is the annual rate of return earned on the investment?

A)7.3%
B)8.2%
C)9.5%
D)10.8%
E)11.7%

Question 40

If Rachel invests $1700 today in an account that pays 6 percent interest compounded annually, how long will it take for her to accumulate $6,500 in her account?

A)23.02 years
B)18.50 years
C)20.52 years
D)16.89 years
E)25.65 years

Question 41

The effective annual rate (rEAR) considers the effect of compounding, whereas annual percentage rate (APR) does not consider the effect of compounding. 

Question 42

Everything else equal, the greater the number of compounding periods per year, the greater the effective rate of return that is earned on an investment. 

Question 43

Kim has just graduated from law school. She had taken an education loan of $45,000, which now must be repaid in equal monthly installments over the next six years. What is the amount of the monthly loan repayment, if the loan carries a simple annual interest of 5 percent? The first payment will be made in one month. 

A)$689.76
B)$721.71
C)$702.46
D)$658.92
E)$724.72

Question 44

The present value of an investment increases as the opportunity cost rate increases. 

Question 45

The rate of return on the best available alternative investment of equal risk is the risk-adjusted required rate of return. 

Question 46

The effective annual rate of an investment is equal to its quoted interest rate when the investment is compounded _____. 

A)continuously
B)daily
C)monthly
D)semi-annually
E)annually

Question 47

Ordinary annuity is an annuity with payments that occur at the beginning of each period. 

Question 48

David borrowed $120,000 for his business to be repaid in six equal annual installment. The lender charges 6.5 percent interest on the amount of the loan balance that is outstanding at the beginning of each year. The interest component in the amount of the annual installment will be the smallest at the end of:

A)sixth year.
B)first year.
C)third year.
D)fourth year.
E)fifth year.

Question 49

A leading bank offers an investment that pays 8 percent interest, compounded semiannually. What is the investment's effective annual rate (rEAR)?

A)8.16%
B)8.36%
C)8.56%
D)8.76%
E)8.96%

Question 50

Mira has saved $25,000 over the years and she has the option of investing it in either of the two investment plans. Investment A offers 12 percent interest compounded monthly, whereas Investment B pays 13 percent interest compounded semiannually. What would be the difference between the future values of the two investments if Mira's investment horizon is seven years?

A)$4,204.52
B)$3,577.87
C)$1,152.34
D)$2,703.78
E)$3,250.22

Question 51

Ross purchased a new commercial vehicle today for $25,000. The entire amount was financed using a five-year loan with a 4 percent interest rate (compounded monthly). How much will Ross owe on his vehicle loan after making payments for three years (i.e., when two years of payments remain)?

A)$10,089.56
B)$10,602.44
C)$10,857.28
D)$11,345.77
E)$11,568.25

Question 52

If a loan is to be repaid in equal periodic amounts (monthly, quarterly, or annually), it is said to be an amortized loan. 

Question 53

Gale Corporation leases the printing equipment it uses. The terms of the lease require the monthly lease payments to be made at the beginning of every month. This is an example of an annuity due. 

Question 54

Identify the correct expression for the effective annual rate (EAR). 

A)(1 + Periodic rate of interest)Number of borrowing (interest) periods in one year - 1
B)(1 / Periodic rate of interest)Number of borrowing (interest) periods in one year - 1
C)(1 - Periodic rate of interest)Number of borrowing (interest) periods in one year - 1
D)(1 + Periodic rate of interest)Number of borrowing (interest) periods in one year + 1
E)(1 - Periodic rate of interest)Number of borrowing (interest) periods in one year + 1

Question 55

An investment carries an interest rate of 8 percent compounded annually. When using the time value of money functions of a financial calculator, the interest rate is entered as 8, whereas it is entered as 0.08 when using a spreadsheet to make the time value of money calculations. 

Question 56

The present value of an uneven cash flow can be determined by using the annuity equations. 

Question 57

If Alvin invests $5,500 today in a savings account, the money will grow to $8,500 at the end of Year 4. Assuming that the interest is paid once per year, the effective annual rate of the investment is _____. 

A)10.8%
B)11.5%
C)12.2%
D)12.9%
E)13.6%

Question 58

Frank purchased his house 16 years ago by taking out a 25-year mortgage for $150,000. The mortgage has a fixed interest rate of 5 percent compounded monthly. If he wants to pay off his mortgage today, how much money does he need? He made his most recent mortgage payment earlier today. (Round your intermediate calculation and your answer to two decimal places.)

A)$65,459.98
B)$70,856.65
C)$76,136.95
D)$80,425.21
E)$85,024.66