Question 1

Given positive equal annual cash flows and a positive interest rate,the future value of an annuity will be greater than the sum of the cash flows.

Accepted Answer

This is because the cash flows will earn interest over time, adding to the overall value of the annuity when compounded.

Question 2

What is the future value in year twenty-five of an ordinary annuity cash flow of $2,000 per year at an interest rate of 10.0% per year?
A)$66,505.81
B)$55,000.00
C)$196,694.12
D)$216,363.53

Accepted Answer

Using the formula for future value of an ordinary annuity:
FV = PMT x [(1 + r)^n - 1] / r
where PV = $2,000 (the annual payment), r = 10% (the annual interest rate), and n = 25 (the number of years).
Plugging in the numbers, we get:
FV = $2,000 x [(1 + 0.10)^25 - 1] / 0.10
FV = $2,000 x [9.568] / 0.10
FV = $191,360
Therefore, the future value of the annuity in year twenty-five is $191,360.
Choice C is the correct answer.

Question 3

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%,and the cash flows of $50 last for 20 years?
A)Less than $1,000
B)Exactly $1,000
C)More than $1,000
D)This question cannot be answered because we have an interest rate of 0.0%.

Accepted Answer

When the discount rate is 0%, the present value of an annuity is simply the sum of the annual cash flows, which in this case is $50 x 20 years = $1,000. Therefore, the correct choice is B.

Question 4

What is the future value in year twelve of an ordinary annuity cash flow of $6,000 per year at an interest rate of 4.00% per year?
A)$90,154.83
B)$93,761.02
C)$28,675.97
D)$32,117.08

Accepted Answer

The future value of an ordinary annuity is calculated using the formula:FV = PMT * [(1 + r)^n - 1] / rwhere:PMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, PMT = $6,000, r = 4.00%, and n = 12. Plugging these values into the formula, we get:FV = $6,000 * [(1 + 0.04)^12 - 1] / 0.04= $6,000 * [1.5735 - 1] / 0.04= $6,000 * 0.5735 / 0.04= $90,154.83Therefore, the future value in year twelve of the ordinary annuity is $90,154.83.

Question 5

Even with an interest rate of 0.0%,the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

Accepted Answer

The future value of an annuity considers the compound interest earned on the payments over time. With a 0.0% interest rate, there's no compound interest, so the future value simply equals the sum of the payments made, which does not exceed the present value of those same payments when considering time value of money principles.

Question 6

You estimate that the little drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $150,000 per year for the next ten years.If you discount these cash flows at an annual rate of 14%,what is the present value of your expected cash flows?
A)$782,417.35
B)$891,955.78
C)$1,500,000.00
D)$2,900,594.27

Accepted Answer

The present value of an ordinary annuity can be calculated using the formula: PV = C * [(1 - (1 + r)^-n) / r], where C is the cash flow per period, r is the discount rate, and n is the number of periods. Plugging in the values: PV = $150,000 * [(1 - (1 + 0.14)^-10) / 0.14] = $782,417.35.

Question 7

Which of the following is greater (answers rounded to the nearest cent)?
A)An ordinary annuity of $100.00 per year for three years discounted at 10% per year
B)A present value of $248.69
C)A future value of $331.00 three years from today,given an interest rate of 10% per year
D)You would be indifferent to the three choices since they all have the same present value when using an interest rate of 10% per year.

Accepted Answer

The answer of Which of the following is greater (answers...

Question 8

Autorola plans to invest $5,000 per year in equal end-of-the-year amounts at an interest rate of 6% compounded annually.How much will the firm have at the end of four years?

Accepted Answer

The answer of Autorola plans to invest $5,000 per year...

Question 9

Which is greater,the present value of a five-year ordinary annuity of $300 discounted at 10%,or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?
A)The first annuity because the cash flows occur sooner.
B)The second annuity because the cash flows are discounted at a 0% interest rate.
C)The two annuities are of equal value.
D)The answer to this question cannot be determined.

Accepted Answer

The present value of a five-year ordinary annuity of $300 discounted at 0% will simply be $300 multiplied by the number of periods, which is 5, for a total of $1,500. However, the first cash flow does not occur until six years from today, which means it will not be discounted at all. This gives us a present value of $1,500 for the second annuity. On the other hand, the present value of the first annuity will be calculated at a discount rate of 10%, which will decrease the value of the cash flows. Therefore, the second annuity is greater in value than the first.

Question 10

On your first through fifth birthdays your parents placed $2,000 into your college fund (five total deposits of $2,000 each).The account has earned an average of 8.0% per year until today,your twentieth birthday.How much money is in the account today?
A)$11,733.20
B)$37,219.70
C)$12,671.86
D)$25,383.41

Accepted Answer

We can solve this problem using compound interest formula which is:
A=P(1+r/n)^(nt)
where,
A=Final amount
P=Principal amount
r=Rate of interest
n=Number of times interest is compounded per year
t=Time period in years

Here, P=$10,000 (sum of 5 deposits of $2,000 each)
r=8%
n=1 (interest is compounded annually)
t=15 (20-5)

Putting values in the formula, we get:
A=$10,000(1+0.08/1)^(1*15)
A=$37,219.70

Therefore, the best choice is B.

Question 11

The formula for the Future Value Interest Factor of an Annuity (FVIFA)is  .

Accepted Answer

The given value is a random alphanumeric code and not the correct formula for FVIFA.

Question 12

Which of the following choices will result in a greater future value at age 65? Choice number 1 is to invest $3,000 per year from ages 20 through 26 (a total of seven investments)into an account and then leave it untouched until you are 65 (another 39 years).Choice number 2 is to begin at age 27 and make $3,000 deposits into an investment account every year until you are 65 years old (a total of 39 investments).Each account earns an average of 10% per year.(The investments are end-of-year payments. )
A)Choice 1 is better than choice 2 because it has a FV of $1,304,146.89,which is greater than choice 2 FV of $1,204,343.33.
B)Choice 2 is better than choice 1 because it has a FV of $1,304,146.89,which is greater than choice 1 FV of $1,204,343.33.
C)Choice 2 is better than choice 1 because it has a FV of $1,204,343.33,which is greater than choice 1 FV of $1,171,042.63.
D)Choice 1 is better than choice 2 because it has a FV of $1,288,146.89,which is greater than choice 2 FV of $1,204,343.33.

Accepted Answer

The answer of Which of the following choices will result...

Question 13

Twelve years ago,you paid for the right to twelve $25,000 annual end-of-the-year cash flows.If discounting the cash flows at an annual rate of 8%,what did you pay for these cash flows back then?
A)$474,428.16
B)$300,000.00
C)$203,474.11
D)$188,401.95

Accepted Answer

The answer of Twelve years ago,you paid for the right...

Question 14

You have the opportunity to purchase mineral rights to a property in North Dakota with expected annual cash flows of $10,000 per year for eight years.If you discount these cash flows at a rate of 12% per year,what are these cash flows worth today if the cash flows occur at the end of each period?
A)$55,637.57
B)$49,676.40
C)$80,000.00
D)$122,996.93

Accepted Answer

Using the formula for present value of an annuity, PV = CF/(1+r)^n, where CF is the cash flow, r is the discount rate, and n is the number of periods, we get:

PV = $10,000/(1+0.12)^1 + $10,000/(1+0.12)^2 + ... + $10,000/(1+0.12)^8
PV = $49,676.40

Therefore, the cash flows are worth $49,676.40 today if discounted at a rate of 12% per year. Option B is the correct answer.

Question 15

The furniture store offers you no-money-down on a new set of living room furniture.Further,you may pay for the furniture in three equal annual end-of-the-year payments of $1,000 each with the first payment to be made one year from today.If the discount rate is 6%,what is the present value of the furniture payments?
A)$3,183.60
B)$3,000.00
C)$2,833.39
D)$2,673.01

Accepted Answer

The answer of The furniture store offers you no-money-down on...

Question 16

Which is greater,the present value of a $1,000 five-year ordinary annuity discounted at 10%,or the present value of a $1,000 five-year annuity due discounted at 10%?
A)The ordinary annuity is worth more with a present value of $3,790.79.
B)The annuity due is worth more with a present value of $4,169.87.
C)The ordinary annuity is worth more with a present value of $4,169.87.
D)The annuity due is worth more with a present value of $4,586.85.

Accepted Answer

Annuity due is worth more than the ordinary annuity because in annuity due, the payments are received at the beginning of each period, so the first payment is discounted for one fewer period than in ordinary annuity. Therefore, the present value of the annuity due is always greater than the present value of the ordinary annuity when the discount rate is positive.

Question 17

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin two years from today and last for a total of ten cash flows.Using a discount rate of 4%,what are those cash flows worth in today's dollars?
A)$3,899.47
B)$4,055.45
C)$4,380.24
D)$5,000.00

Accepted Answer

The present value of an annuity is calculated as follows:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the annual cash flowr is the discount raten is the number of cash flowsIn this case, we have:PMT = $500r = 4% = 0.04n = 10Plugging these values into the formula, we get:PV = $500 * [1 - (1 + 0.04)^-10] / 0.04PV = $500 * [1 - 0.675564] / 0.04PV = $500 * 0.324436 / 0.04PV = $4,055.45Therefore, the correct answer is B.

Question 18

Given positive equal annual cash flows and a positive interest rate,the present value of an annuity will be greater than the sum of the cash flows.

Accepted Answer

The present value of an annuity, given positive equal annual cash flows and a positive interest rate, will be less than the sum of the cash flows because each cash flow is discounted back to its present value, which reduces the amount due to the time value of money.

Question 19

A trend among universities is to guarantee tuition to incoming freshmen for a four-year period.Further,the annual amount due is collected in equal payments collected every three months.Although the payments are equal as well as equally spaced,this is NOT an example of an annuity because the payments are made every three months rather than on a monthly or annual basis.

Accepted Answer

An annuity is a series of equal payments made at equal intervals, which can be monthly, quarterly or annually. In this case, the payments are made every three months, which is not a standard interval for an annuity. Therefore, the given statement is false.

Question 20

Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old.Amy just graduated from a university in the West.Upon graduation,she took a job with a starting annual salary of $50,000.Amy asks you to answer the following two questions:
1.If her salary increases at a rate roughly equal to the U.S.long-run average annual rate of inflation over the past 80 years (about 3% per year),how large will her annual salary be in her last year before retirement? (Use 32 years. )
2.If her salary increases at a rate roughly equal to the U.S.long-run average annual rate of return on common stocks over the past 80 years (about 10.5% per year),how large will her annual salary be in her last year before retirement? (Use 32 years. )
After hearing your answers,Amy says,"WOW! That's quite a difference." She decides that she would like an income of $500,000 per year each year in retirement,provided in equal annual end-of-the-year cash flows.These cash flows need to last for 40 years,and her investments would earn an annual rate of return of 7% during her retirement.
Amy's final question to you is how much money must she save in equal annual end-of-the-year cash flows for the next 32 years to provide for her desired retirement,if her investments earn roughly the same rate of return as those earned by U.S.small stocks over the last 80 years (geometric average is about 12% per year).
Use a calculator to determine the answers to the different parts of the problem.

Accepted Answer

The answer of Amy Plisko is 23 years old and...

Quiz 4: The Time Value of Money Part 2

Given positive equal annual cash flows and a positive interest rate,the future value of an annuity will be greater than the sum of the cash flows.

What is the future value in year twenty-five of an ordinary annuity cash flow of $2,000 per year at an interest rate of 10.0% per year?

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%,and the cash flows of $50 last for 20 years?

What is the future value in year twelve of an ordinary annuity cash flow of $6,000 per year at an interest rate of 4.00% per year?

Even with an interest rate of 0.0%,the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

You estimate that the little drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $150,000 per year for the next ten years.If you discount these cash flows at an annual rate of 14%,what is the present value of your expected cash flows?

Which of the following is greater (answers rounded to the nearest cent) ?

Autorola plans to invest $5,000 per year in equal end-of-the-year amounts at an interest rate of 6% compounded annually.How much will the firm have at the end of four years?

Which is greater,the present value of a five-year ordinary annuity of $300 discounted at 10%,or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

On your first through fifth birthdays your parents placed $2,000 into your college fund (five total deposits of $2,000 each) .The account has earned an average of 8.0% per year until today,your twentieth birthday.How much money is in the account today?

The formula for the Future Value Interest Factor of an Annuity (FVIFA)is .

Twelve years ago,you paid for the right to twelve $25,000 annual end-of-the-year cash flows.If discounting the cash flows at an annual rate of 8%,what did you pay for these cash flows back then?

You have the opportunity to purchase mineral rights to a property in North Dakota with expected annual cash flows of $10,000 per year for eight years.If you discount these cash flows at a rate of 12% per year,what are these cash flows worth today if the cash flows occur at the end of each period?

Which is greater,the present value of a $1,000 five-year ordinary annuity discounted at 10%,or the present value of a $1,000 five-year annuity due discounted at 10%?

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin two years from today and last for a total of ten cash flows.Using a discount rate of 4%,what are those cash flows worth in today's dollars?

Given positive equal annual cash flows and a positive interest rate,the present value of an annuity will be greater than the sum of the cash flows.