Question 1

If you invest $2,500 in a bank account that pays 6% interest compounded quarterly,how much will you have in five years?

Accepted Answer

P/YR = 4
PV = 2,500
I/YR = 6
N = 20
FV = ? = 3,367.14

Question 2

A stainless steel products manufacturer with an 8.5% cost of capital receives a $3,000,000 order,payable at the end of three years.What is the annual payment amount made at the end of each year with the equivalent present value?

Accepted Answer

FV = 3,000,000
I/YR = 8.5
N = 3
PMT = ? = 919,618

Question 3

Having acquired great fortune based on your mastery of finance,you decide to set up a charity.You'd like to give the finance department of your alma mater $100,000 next year,and you want to make an annual contribution in perpetuity,with each year's contribution growing by 4%.The university can generate an 8% return on invested capital.What is the value of a lump-sum donation needed today to accomplish this?

Accepted Answer

PV = CF1/(r - g)
PV = 100,000/(.08 - .04)= 2,500,000

Question 4

Your firm rents office space for $250,000 per year,due at the BEGINNING of each year.If your firm's hurdle rate is 10%,what is the present value of five years' worth of rent?

Accepted Answer

BEG Mode
PMT = 250,000
I/YR = 10
N = 5
PV = ? = 1,042,466.36

Question 5

Great Lakes Christmas Tree Co.expects to pay an annual dividend of $2 per share in perpetuity on its preferred shares starting one year from now.The firm is committed solely to its steady North American Christmas tree business (as opposed to,say,diversifying into landscape shrubbery).This profile warrants a required return of 6%.What is the present value of this dividend stream for investors?

Accepted Answer

PV = CF/r
PV = 2/.06 = 33.33

Question 6

Calculate the monthly payment for a 20-year mortgage on a $3.5 million building at a 7.5% interest rate.Assume that the entire building is financed and that payments are made at the end of each month,starting at the end of the first month and ending at the end of the last month.

Accepted Answer

P/YR = 12
PV = 3,500,000
I/YR = 7.5
N = 240
PMT = ? = 28,195.76

Question 7

You inherit $15,000 from your aunt.You decide to invest the money in a three-year CD that pays 4% interest to use as a down payment on a house.How much money will you have when the CD matures?

Accepted Answer

PV = 15,000
N = 3
I/YR = 4
FV = ? = 16,872.96

Question 8

You buy a house for $220,000 in a neighborhood where home prices have risen 5% annually on average.You suspect that growth in home prices will slow to an average of 3.5% per year over the next five years.If your growth estimate of 3.5% growth is correct,how much less will your house be worth in five years compared with 5% growth?

Accepted Answer

PV = 220,000
N = 5
I/YR = 5
FV = 280,781.94
PV = 220,000
N = 5
I/YR = 3.5
FV = 261,290.99
$280,781.94 - $261,290.99 = $19,490.95

Question 9

Atlas Map Co.has purchased a new building for $45 million.If the value of the building increases at a rate of 5% per year,how much will the building be worth in 20 years?

Accepted Answer

PV = 45,000,000
I/YR = 5
N = 20
FV = ? = 119,398,397

Question 10

Calculate the annual payment for a 20-year mortgage on a $3.5 million building at a 7.5% interest rate.Assume that the entire building is financed and that payments are made at the end of each year,starting at the end of the first year and ending at the end of the 20th year.

Accepted Answer

PV = 3,500,000
I/YR = 7.5
N = 20
PMT = ? = 343,322.67

Question 11

If you deposit $9,000 at the BEGINNING of each year in an account earning 8% interest,what will be the value of the account in 25 years?

Accepted Answer

BEG Mode
PV = 9,000
I/YR = 10
N = 25
FV = ? = 710,589.74

Question 12

You decide that your family would be comfortable living on an annual income of $150,000,growing at 4% per year.You'd also like to continue generating this cash flow for your descendents,forever.With investment returns of 8%,how much wealth would you need today to provide this income starting with $150,000 one year from now?

Accepted Answer

PV = CF!/(r - g)
PV = 150,000/(.08 - .04)= 3,750,000

Question 13

You would like to retire with $1 million on your 60th birthday.If you start saving equal annual amounts on your 26th birthday,make your last deposit on your 60th birthday,and earn 10% interest on your money,how much must you invest each year to achieve your goal?

Accepted Answer

FV = 1,000,000
I/YR = 10
N = 35
PMT = ? = 3,689.71

Question 14

If you need $35,000 for a down payment on a house in six years,how much money must you invest today at 7% interest compounded annually to achieve your goal?

Accepted Answer

FV = 35,000
N - 6
I/YR = 7
PV = ? = $23,321.98

Question 15

A $200 investment in an account that pays 7% continuous interest would be worth how much in twenty years?

Accepted Answer

= $200 *e^(.07*20)

Question 16

If you deposit $9,000 at the end of each year in an account earning 8% interest,what will be the value of the account in 25 years?

Accepted Answer

PMT = 9,000
N = 25
I/YR = 8
FV = ? = 710,589.74

Question 17

If you invest $5,000 in a mutual fund with a total annual return (interest rate)of 8% and you re-invest the proceeds each year,what will be the value of your investment after five years?

Accepted Answer

PV = 5,000
N = 5
I/YR = 8
FV = ? = 7,346.64

Question 18

Your credit card carries a 9.9% annual percentage rate,compounded daily.What is the effective annual rate,or annual percentage yield?

Accepted Answer

(1 + .099/365)³⁶⁵ - 1 = 10.41%

Question 19

Your firm is evaluating a project that should generate revenue of $4,600 in year 1,$5,200 in year two,$5,900 in year three,and $5,700 in year four.The firm receives each cash flow at the end of each year.If your firm's required return is 12%,what is the future value of these cash flows at the end of year four?

Accepted Answer

CF0 = 0
CF1 = 4,600
CF2 = 5,200
CF3 = 5,900
CF4 = 5,700
I/YR = 12
NPV = ? = 16,074.51
PV = 16,074.51
N = 4
I = 12
FV = ? = 25,293.55

Question 20

A report from the marketing department indicates that a new product will generate the following revenue stream: $62,500 in the first year,$89,400 in year two,$136,200 in year three,$128,300 in year four,and $112,000 in year five.If your firm's discount rate is 11% and the cash flows are received at the end of each year,what is the present value of this cash flow stream?

Accepted Answer

CF0 = 0
CF1 = 62,500
CF2 = 89,400
CF3 = 136,200
CF4 = 128,300
CF5 = 112,000
I/YR = 11
NPV = ? = 379,435.35

Quiz 3: The Time Value of Money