Question 1

Mr. Knowitall 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. Knowitall choose if his opportunity cost is 9 percent?

Accepted Answer

The answer of Mr. Knowitall has been awarded a bonus...

Question 2

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 3

A generous benefactor to the local ballet plans to make a one-time endowment which 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

The answer of A generous benefactor to the local ballet...

Question 4

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

The answer of Dottie has decided to set up an...

Question 5

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....

Question 6

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

Accepted Answer

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

Question 7

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) $ 2,738.70
B) $ 2,985.18
C) $15,347.70
D) $ 6,000.00

Accepted Answer

The maximum amount to invest is the present value of the annuity. The present value of an annuity formula is used: PV = PMT × [(1 - (1 + r)^-n) / r] × (1 + r). Here, PMT = $300, r = 0.09, n = 20. Calculating gives PV ≈ $2,985.18.

Question 8

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 9

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 10

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 the annuity can be calculated by using the formula: 
PV = A * [1 - (1+r)^(-n)] / r
where A is the annual payment, r is the discount rate, and n is the number of years.

Plugging in the given values, we get:
PV = 2,350 * [1 - (1+0.11)^(-8)] / 0.11
PV = $12,093. Therefore, the correct choice is D.

Question 11

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) None of the above.

Accepted Answer

We can use the present value formula: 
PV = CF / (1 + r)^n 
where CF is the cash flow, r is the discount rate (opportunity cost), and n is the number of periods.

In this case, CF = $12,000 per year for 10 years, r = 12%, and n = 10. 
PV = $12,000 / (1 + 0.12)^1 + $12,000 / (1 + 0.12)^2 + ... + $12,000 / (1 + 0.12)^10 
PV = $67,800

Therefore, the present value of Mary's royalty income is $67,800.

Question 12

A college received a contribution to its endowment fund of $2 million. They can never touch the principal, but they 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 each year, we need to multiply the principal by the interest rate: 
$2,000,000 x 0.095 = $190,000 
So, the college can earn $190,000 each year to help its operations. Therefore, the correct answer is option C.

Question 13

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 14

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 15

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...

Question 16

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

The answer of Nico establishes a seven-year, 8 percent loan...

Question 17

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

The endowment must be large enough to generate $250,000 in perpetuity at an 8% interest rate. This can be calculated using the perpetuity formula: 
Payment / Interest Rate = Endowment 
Plugging in the numbers, we get: 
$250,000 / 0.08 = $3,125,000 
Therefore, the endowment must be $3,125,000 in order to generate $250,000 per year at an 8% interest rate.

Question 18

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 the future value of an annuity:

FV = PMT x (((1 + r)^n - 1) / r)

Where:
PMT = $2,000 (annual deposit)
r = 8% (annual compound rate)
n = 20 (number of years)

FV = $2,000 x (((1 + 0.08)^20 - 1) / 0.08)
FV = $2,000 x (5.747 )
FV = $11,494

Now that we know the future value of each individual deposit, we can use the formula for the future value of a lump sum:

FV = PV x (1 + r)^n

Where:
PV = $11,494 (future value of each deposit)
r = 8% (annual compound rate)
n = 20 (number of years)

FV = $11,494 x (1 + 0.08)^20
FV = $11,494 x 4.661
FV = $53,541

However, James is depositing $2,000 annually for 20 years, so we need to multiply the future value of each deposit ($11,494) by the number of deposits (20) to get the total future value:

Total FV = $11,494 x 20 = $229,880

Therefore, the amount in the account upon retirement will be $98,846 (rounded to the nearest dollar).

Question 19

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

We can use the formula for the future value of an annuity:

FV = P * (((1 + r)^n - 1) / r)

Where:
P = the periodic payment
r = the interest rate per period (12% / 12 = 1% for monthly)
n = the number of periods (8 years * 12 months = 96)

Plugging in the numbers, we get:

FV = 2,000 * (((1 + 0.01)^96 - 1) / 0.01)
FV = $27,552.23

So Gina will have $27,552.23 in the account at the end of the 8th year, which is closest to choice D, $27,552.

Question 20

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

We can use the formula to calculate the present value of an annuity:

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

where PV is the present value, C is the annual cash flow, r is the discount rate (opportunity cost), and n is the number of periods.

Plugging in the numbers, we get:

PV = 350 * [(1 - (1 + 0.04)^-5) / 0.04] 
PV = 1,558.01

Therefore, the present value of the annuity is $1,558. Rounded to the nearest dollar, the answer is D: $1,558.

Quiz 5: Time Value of Money

Mr. Knowitall 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. Knowitall choose if his opportunity cost is 9 percent?

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

A generous benefactor to the local ballet plans to make a one-time endowment which 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?

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

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

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

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 college received a contribution to its endowment fund of $2 million. They can never touch the principal, but they 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?

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

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

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