Question 1

If the present value of a perpetual income stream is increasing,the discount rate must be ________.
A) increasing
B) decreasing
C) changing unpredictably
D) increasing proportionally

Accepted Answer

The present value of a perpetual income stream increases when the discount rate decreases, as the present value is inversely related to the discount rate.

Question 2

Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book.What is the present value of her royalty income if the opportunity cost is 12 percent?
A) $120,000
B) $ 67,800
C) $ 38,640
D) $ 72,560

Accepted Answer

The present value can be calculated using the formula: PV = C x [1 - (1 + r)^(-n)] / r
where C is the annual cash flow ($12,000), r is the discount rate (12% or 0.12), and n is the number of years (10).
Substituting the values, we get:
PV = 12,000 x [1 - (1 + 0.12)^(-10)] / 0.12 = $67,800. Therefore, the present value of Mary's royalty income is $67,800.

Question 3

Calculate the present value of an annuity of $3,900 each year for four years,assuming an opportunity cost of 10 percent.

Accepted Answer

The answer of Calculate the present value of an annuity...

Question 4

A college received a contribution to its endowment fund of $2 million.It can never touch the principal,but can use the earnings.At an assumed interest rate of 9.5 percent,how much can the college earn to help its operations each year?
A) $95,000
B) $19,000
C) $190,000
D) $18,000

Accepted Answer

To find out how much the college can earn to help its operations each year, we need to find 9.5% of the principal amount, which is $2 million. 
9.5% of $2 million = 0.095 x $2,000,000 = $190,000. 
Therefore, the answer is C, $190,000.

Question 5

Mr.Jackson has been awarded a bonus for his outstanding work.His employer offers him a choice of a lump-sum of $5,000 today,or an annuity of $1,250 a year for the next five years.Which option should Mr.Jackson choose if his opportunity cost is 9 percent?

Accepted Answer

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Question 6

You have been offered a project paying $300 at the beginning of each year for the next 20 years.What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?
A) $ 2,738
B) $ 2,985
C) $15,347
D) $ 6,000

Accepted Answer

To calculate the maximum amount to invest, we need to find the present value of the cash flows at a discount rate of 9%. Using the formula for the present value of an annuity, we get:

PV = C[1 - (1 + r)^-n]/r
where PV is the present value, C is the annual cash flow ($300), r is the discount rate (9%), and n is the number of years (20).

Plugging in the values, we get:
PV = $300[1 - (1 + 0.09)^-20]/0.09
PV = $2,985.09

Therefore, the maximum amount to invest in this project is $2,985. Any amount higher than this will result in a negative rate of return.

Question 7

Calculate the future value of an annuity of $5,000 each year for eight years,deposited at 6 percent.

Accepted Answer

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Question 8

A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with $150,000 per year into perpetuity.The rate of interest is expected to be 5 percent for all future time periods.How large must the endowment be?
A) $ 300,000
B) $3,000,000
C) $ 750,000
D) $1,428,571

Accepted Answer

To find the size of the endowment needed to provide $150,000 per year into perpetuity at an interest rate of 5%, you use the formula for perpetuity: Endowment = Annual Payment / Interest Rate. Plugging in the numbers: Endowment = $150,000 / 0.05 = $3,000,000.

Question 9

Dottie has decided to set up an account that will pay her granddaughter (Lexi)$5,000 a year indefinitely.How much should Dottie deposit in an account paying 8 percent annual interest?

Accepted Answer

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Question 10

Jia has just won a $20 million lottery,which will pay her $1 million at the end of each year for 20 years.An investor has offered her $10 million for this annuity.She estimates that she can earn 10 percent interest,compounded annually,on any amounts she invests.She asks your advice on whether to accept or reject the offer.What will you tell her? (Ignore Taxes)

Accepted Answer

The answer of Jia has just won a $20 million...

Question 11

The present value of an ordinary annuity of $2,350 each year for eight years,assuming an opportunity cost of 11 percent,is ________.
A) $ 1,020
B) $27,869
C) $18,800
D) $12,093

Accepted Answer

The present value of an ordinary annuity formula is:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present Value
C = Cash Flow per period
r = Opportunity cost or discount rate
n = Number of periods

Using the given values:

PV = $2,350 * [(1 - (1 + 0.11)^(-8)) / 0.11]
PV = $2,350 * [(1 - 0.31799) / 0.11]
PV = $2,350 * 6.2372
PV = $14,668.82

Therefore, the present value of the annuity is $14,668.82, which corresponds to option D.

Question 12

To pay for her college education,Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest.How much will Gina have in that account at the end of 8th year?
A) $16,000
B) $17,920
C) $24,600
D) $27,552

Accepted Answer

To find out how much Gina will have in the account at the end of 8 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the total amount after 8 years
P = the principal amount (the amount Gina initially saves each year)
r = the annual interest rate (12%)
n = the number of times the interest is compounded per year (since we know the interest rate is annual, we can assume the interest is compounded once per year)
t = the number of years

Plugging in the values we know, we get:

A = 2,000(1 + 0.12/1)^(1*8)
A = 2,000(1.12)^8
A = 2,000(2.44140625)
A = $4,882.81

But we need to add up the total amount saved over the 8 years, which is simply:

Total savings = $2,000 x 8 = $16,000

So the total amount Gina will have in the account at the end of 8 years is:

$4,882.81 + $16,000 = $20,882.81, which is closest to answer choice D: $27,552.

Question 13

The present value of an ordinary annuity of $350 each year for five years,assuming an opportunity cost of 4 percent,is ________.
A) $288
B) $1,896
C) $1,750
D) $1,558

Accepted Answer

Using the present value of an ordinary annuity formula, PV = C * ((1 - (1+r)^(-n))/r), where C is the annual payment, r is the interest rate, and n is the number of payments, we can calculate the present value of the annuity to be PV = $350 * ((1 - (1+0.04)^(-5))/0.04) = $1,558. Therefore, the best choice is D, which matches this calculated value.

Question 14

Nico establishes a seven-year,8 percent loan with a bank requiring annual end-of-year payments of $960.43.Calculate the original principal amount.

Accepted Answer

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Question 15

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity.The rate of interest is expected to be 8 percent for all future time periods.How large must the endowment be?
A) $2,314,814
B) $2,000,000
C) $3,125,000
D) $3,000,000

Accepted Answer

To calculate the present value of perpetuity, we divide the annual payment by the rate of interest. In this case, the annual payment is $250,000 and the rate of interest is 8%, so the present value of perpetuity is:

PV = $250,000 / 0.08 = $3,125,000

Therefore, the endowment must be $3,125,000.

Question 16

A lottery administrator has just completed the state's most recent $50 million lottery.Receipts from lottery sales were $50 million and the payout will be $5 million at the end of each year for 10 years.The expenses of running the lottery were $800,000.The state can earn an annual compound rate of 8 percent on any funds invested.
(a)Calculate the gross profit to the state from this lottery.
(b)Calculate the net profit to the state from this lottery (no taxes).

Accepted Answer

The answer of A lottery administrator has just completed the...

Question 17

James plans to fund his individual retirement account,beginning today,with 20 annual deposits of $2,000,which he will continue for the next 20 years.If he can earn an annual compound rate of 8 percent on his deposits,the amount in the account upon retirement will be ________.
A) $19,636
B) $91,524
C) $98,846
D) $21,207

Accepted Answer

Using the formula for future value of an annuity:
FV = Pmt x (((1 + r)^n - 1) / r)
Where:
Pmt = $2,000 (annual deposit)
r = 8% (annual interest rate)
n = 20 (number of deposits)
We can calculate the future value of James' retirement account:
FV = $2,000 x (((1 + 0.08)^20 - 1) / 0.08) = $98,846.

Question 18

In their meeting with their advisor,Mr.and Mrs.O'Rourke concluded that they would need $40,000 per year during their retirement years in order to live comfortably.They will retire 10 years from now and expect a 20-year retirement period.How much should Mr.and Mrs.O'Rourke deposit now in a bank account paying 9 percent to reach financial happiness during retirement?

Accepted Answer

The answer of In their meeting with their advisor,Mr.and Mrs.O'Rourke...

Question 19

A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income for his grandchild into perpetuity.He stipulates in the trust agreement that the principal may not be distributed.The grandchild may only receive the interest earned.If the interest rate earned on the trust is expected to be at least 7 percent in all future periods,how much income will the grandchild receive each year?

Accepted Answer

The answer of A wealthy industrialist wishes to establish a...

Question 20

Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.

Accepted Answer

The answer of Calculate the present value of a $10,000...

Quiz 5: Time Value of Money

If the present value of a perpetual income stream is increasing,the discount rate must be ________.

Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book.What is the present value of her royalty income if the opportunity cost is 12 percent?

Calculate the present value of an annuity of $3,900 each year for four years,assuming an opportunity cost of 10 percent.

A college received a contribution to its endowment fund of $2 million.It can never touch the principal,but can use the earnings.At an assumed interest rate of 9.5 percent,how much can the college earn to help its operations each year?

Mr.Jackson has been awarded a bonus for his outstanding work.His employer offers him a choice of a lump-sum of $5,000 today,or an annuity of $1,250 a year for the next five years.Which option should Mr.Jackson choose if his opportunity cost is 9 percent?

You have been offered a project paying $300 at the beginning of each year for the next 20 years.What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?

Calculate the future value of an annuity of $5,000 each year for eight years,deposited at 6 percent.

A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with $150,000 per year into perpetuity.The rate of interest is expected to be 5 percent for all future time periods.How large must the endowment be?

Dottie has decided to set up an account that will pay her granddaughter (Lexi)$5,000 a year indefinitely.How much should Dottie deposit in an account paying 8 percent annual interest?

The present value of an ordinary annuity of $2,350 each year for eight years,assuming an opportunity cost of 11 percent,is ________.

To pay for her college education,Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest.How much will Gina have in that account at the end of 8th year?

The present value of an ordinary annuity of $350 each year for five years,assuming an opportunity cost of 4 percent,is ________.

Nico establishes a seven-year,8 percent loan with a bank requiring annual end-of-year payments of $960.43.Calculate the original principal amount.

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity.The rate of interest is expected to be 8 percent for all future time periods.How large must the endowment be?

James plans to fund his individual retirement account,beginning today,with 20 annual deposits of $2,000,which he will continue for the next 20 years.If he can earn an annual compound rate of 8 percent on his deposits,the amount in the account upon retirement will be ________.

Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.