Question 1

You own a contract that promises an annuity cash flow of $100 beginning-of-the-year cash flows for each of the next three years (note: the first cash flow is today).At an interest rate of 10%,what is the future value of this contract exactly three years from today?
A)$248.69
B)$273.55
C)$331.00
D)$364.10

Accepted Answer

The future value of an annuity due can be calculated by compounding each cash flow to the end of the period. The first $100 is compounded for 3 years, the second $100 for 2 years, and the third $100 for 1 year. The future value is $100*(1.1)^3 + $100*(1.1)^2 + $100*(1.1)^1 = $364.10.

Question 2

Your parents paid $1,000 for a college fund bond when you were born.Today is your 20^th birthday and you are ready to cash the bond which has grown to a value of $3,361.85.What was the average annual rate of return on your college fund bond? A)5.50% B)6.25% C)6.73% D)There is not enough information to answer this question.

Accepted Answer

The average annual rate of return can be calculated using the formula for compound interest: $ A = P(1 + r)^n $. Here, $ A = 3361.85 $, $ P = 1000 $, and $ n = 20 $. Solving for $ r $, we find that the rate is approximately 6.25%.

Question 3

You have been accepted into a prestigious private university in Southern California - congratulations! Since no one from this school has ever graduated in only four years,you anticipate that you will need to make 10 semi-annual tuition payments of $25,000 each with the first cash flow six months from today.If you choose to discount these cash flows at an annual rate of 6%,what is the present value cost of tuition to attend your university of choice?
A)$186,814.54
B)$184,002.18
C)$250,000.00
D)$213,255.07

Accepted Answer

D

Question 4

You own a contract that promises an annuity cash flow of $100 beginning-of-the-year cash flows for each of the next three years (note: the first cash flow is today).At an interest rate of 10%,what is the present value of this contract?
A)$248.69
B)$273.55
C)$331.00
D)$364.10

Accepted Answer

To calculate the present value (PV) of the contract, we can use the formula:
PV = (C / (1 + r)^n) + (C / (1 + r)^(n-1)) + ... + (C / (1 + r)^1), where C is the cash flow, r is the interest rate, and n is the number of periods.

In this case, C = $100, r = 10%, and n = 3. Plugging in the values, we get:
PV = ($100 / 1.1) + ($100 / 1.1^2) + ($100 / 1.1^3) = $90.91 + $82.64 + $75.13 = $248.69

Therefore, the best choice is B.

Question 5

You have decided to endow a Chair in Finance at Whatsamatta University.How much money must you deposit into the endowment account today if the Chair pays $125,000 per year (first payment one year from today),increases at a rate of 2% per year forever,and is invested at a rate that pays out 4.50% per year?
A)$2,777,777.78
B)$2,902,777.78
C)$5,000,000.00
D)There is not enough information to answer this question.

Accepted Answer

The answer of You have decided to endow a Chair...

Question 6

Individuals and businesses require compensation for delaying consumption.Which of the following questions may contribute to the magnitude of the compensation?
A)Is there a possibility that the price may increase for the delayed good or service?
B)If current consumption is delayed is it possible that it may not be realized at all?
C)How badly does the firm or individual wish to consume now and what do they require for delaying?
D)All of the above are legitimate reasons to require additional compensation for delaying consumption.

Accepted Answer

All of the above questions are relevant when considering the compensation required for delaying consumption. The possibility of a price increase or loss of the opportunity to consume altogether are factors that increase the value of immediate consumption, while the urgency of current consumption needs versus the benefits of delayed consumption must also be weighed.

Question 7

Your friend has agreed to lend you $5,000 today if you will repay him $5,061.36 in three months.What annual interest rate is your friend charging you for this loan?
A)1.23%
B)5.00%
C)2.47%
D)5.36%

Accepted Answer

The answer of Your friend has agreed to lend you...

Question 8

Peabody Books Inc.wishes to borrow $182,000 today for the purchase of publishing materials.They have an agreement with their commercial banker that they can borrow money at an annual rate of 4.75%.How much will the firm owe if they repay the loan in exactly one year?
A)$8,645
B)$173,747.02
C)$182,000
D)$190,645

Accepted Answer

To calculate the amount owed in one year, you multiply the principal amount by the interest rate and then add the principal back. $182,000 * 4.75% = $8,645 (interest for one year). So, $182,000 + $8,645 = $190,645.

Question 9

What is the present value of $3,500 received 3 years from today if the prevailing interest rate is 6.10%?
A)$2,732.98
B)$2,930.37
C)$3,625.14
D)$4,192.20

Accepted Answer

The present value (PV) of a future amount can be calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate per period, and n is the number of periods. Plugging in the given values: PV = $3,500 / (1 + 0.061)^3 = $2,930.37.

Question 10

You are about to purchase a new car from a dealer who has a new and unusual payment plan.You have the choice to pay $28,000 cash today or $31,000 in four years.If you have the opportunity to borrow the cash price value of the car at a rate of 2.5% and repay the loan in a lump sum in 4 years,which option should you take and why?
A)Pay the $31,000 in the future because it it always better to delay payment for new assets.
B)Pay the $31,000 in the future because the PV is less than $28,000 today.
C)Pay the $28,000 cash today even if you need to borrow the money because the FV of the repayment in 4 years is only $30,906.76.
D)Pay the $28,000 cash today because you pay a full $3,000 less than if you wait and pay the other option as presented.

Accepted Answer

Calculating the Future Value (FV) of borrowing $28,000 for 4 years at a rate of 2.5% using the formula FV = PV x (1 + r)^n, where PV is the present value, r is the interest rate per year, and n is the number of years:
FV = $28,000 x (1 + 0.025)^4
FV = $30,906.76

Comparing the FV of repaying the loan in 4 years ($30,906.76) to the option of paying $31,000 in 4 years, it is evident that paying $28,000 cash today is the better choice since it saves about $2,000. In addition, delaying payment may have additional costs such as interest, inflation, and uncertainty. Therefore, the best option is to pay $28,000 cash today even if you need to borrow the money.

Question 11

You own a contract that promises an annuity cash flow of $100 year-end cash flows for each of the next three years (note: the first cash flow is exactly one year from today).At an interest rate of 10%,what is the present value of this contract?
A)$248.69
B)$273.55
C)$331.00
D)$364.10

Accepted Answer

To calculate the present value of this contract, we need to discount each cash flow back to its present value and then sum them up. Using a discount rate of 10%, we can calculate the present value of each cash flow as follows:

Year 1: $100 / (1 + 0.10)^1 = $90.91
Year 2: $100 / (1 + 0.10)^2 = $82.64
Year 3: $100 / (1 + 0.10)^3 = $75.13

Then, we sum up these present values to get the total present value of the cash flows:

$90.91 + $82.64 + $75.13 = $248.69

Therefore, the best choice is A) $248.69.

Question 12

Your new employer makes you an unusual salary offer.Choice A is to receive a $20,000 lump sum today and another $50,000 in one year.Choice B is to receive nothing today,and $80,000 in one year.You carefully consider what you have learned in your finance class and determine that the risk and uncertainty of this offer as well as the difficulty of having to find money for living expenses for one more year leads you to conclude that the appropriate interest rate at which to evaluate these offers is 40%.Based strictly on the results of your calculations,which offer should you accept and why?
A)Choice A because the present value of $57,142.86 is greater than the PV of $55,714.29 for Choice B.
B)Choice A because the present value of $70,000 is greater than the PV of $57,142.86 for Choice B.
C)Choice B because the present value of $80,000 is greater than the PV of $70,000 for Choice A.
D)Choice B because the present value of $57,142.86 is greater than the PV of $55,714.29 for Choice A.

Accepted Answer

The answer of Your new employer makes you an unusual...

Question 13

Which choice has a greater present value if we assume a required rate of return of 10%? 1: A lump sum cash flow today of $248.69,2: $100 cash flows occurring one,two,and three years from today,or 3: a single cash flow of $331 three years from today.
A)Choice 1
B)Choice 2
C)Choice 3
D)The choices all have equal present values at a discount rate of 10%.

Accepted Answer

To determine the present value (PV) of each choice, we use the formula PV = FV / (1 + r)^n, where FV is the future value, r is the rate of return, and n is the number of periods. For choice 1, the PV is already given as $248.69. For choice 2, the PV of each $100 cash flow is calculated separately for each year and then summed: PV = $100 / (1.1)^1 + $100 / (1.1)^2 + $100 / (1.1)^3 = $90.91 + $82.64 + $75.13 = $248.68. For choice 3, the PV of the $331 cash flow in three years is PV = $331 / (1.1)^3 = $248.69. Thus, all choices have essentially the same present value when rounded, indicating that they are equal in value at a discount rate of 10%.

Question 14

Consider the equation for present value.If you wished to increase the present value of a future amount by changing only one variable,which of the following actions should you take?
A)increase the time period
B)decrease the future value
C)decrease the interest rate
D)This statement cannot be answered with the information provided.

Accepted Answer

The present value of a future amount is inversely proportional to the interest rate. Therefore, decreasing the interest rate will increase the present value. Changing the time period or the future value will not have a direct impact on the present value unless they are also accompanied by a change in the interest rate. Therefore, option C is the best choice to increase the present value of a future amount if only one variable can be changed.

Question 15

Autorola plans to invest money today at an interest rate of 6% compounded annually to have $40,000 available for the purchase of a car four years from now.How much does the firm need to invest today?
A)$50,499.08
B)$36,384.52
C)$31,683.75
D)$9,143.66

Accepted Answer

To find out how much Autorola needs to invest today to have $40,000 available in four years at an interest rate of 6% compounded annually, we use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value (amount to invest today), FV is the future value ($40,000), r is the annual interest rate (6% or 0.06), and n is the number of years (4). Plugging in the values: $PV = \frac{40,000}{(1 + 0.06)^4} = \frac{40,000}{1.262477} = $31,683.75$.

Question 16

If you were able to invest $2,500 at a rate of 6.40% for six months,how much money would you have at the end of that period?
A)$2,349.62
B)$2,423.65
C)$2,578.76
D)$2,660.00

Accepted Answer

The investment grows with interest, which can be calculated using the formula for simple interest: $A = P(1 + rt)$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. For a 6-month period, $t = 0.5$ years. Plugging the values into the formula gives $A = 2500(1 + 0.064 \times 0.5) = 2500(1 + 0.032) = 2500 \times 1.032 = 2580$. The closest answer to this calculation is $2,578.76.

Question 17

You have accumulated $8,000 toward the down payment on a piece of lake front property in rural Minnesota.You wish to accumulate $12,000 for the down payment in four years.If you choose not to contribute more new funds to your down payment fund,what rate of return must your fund earn to reach your objective in the specified time? Assume that your investment fund compounds annually.
A)10.67% per year
B)50.00% per year
C)12.50% per year
D)There is not enough information to answer this question.

Accepted Answer

To calculate the rate of return, we can use the formula: FV = PV x (1 + r)n, where FV is the future value (in this case $12,000), PV is the present value (in this case $8,000), r is the annual interest rate, and n is the number of years (in this case 4). Rearranging the formula to solve for r, we get: r = (FV/PV)^(1/n) - 1. Substituting the values, we get: r = ($12,000/$8,000)^(1/4) - 1 = 0.1067 or 10.67%. Therefore, the answer is A.

Question 18

You have decided to endow a Chair in Finance at Whatsamatta University.How much money must you deposit into the endowment account today if the Chair pays $125,000 per year forever (first payment one year from today)and is invested at a rate that pays out 4.50% per year?
A)$277,777.78
B)$2,902,777.78
C)$2,777,777.78
D)There is not enough information to answer this question.

Accepted Answer

The formula for the present value of perpetuity, which is the value we need to deposit into the endowment account today, is:

PV = PMT / r

Where PV is the present value, PMT is the annual payment ($125,000), and r is the interest rate (4.50%).

Plugging in the values, we get:

PV = $125,000 / 0.045
PV = $2,777,777.78

So we need to deposit $2,777,777.78 into the endowment account today to endow a perpetuity that pays $125,000 per year forever. Therefore, the best choice is C.

Question 19

________ is the cost of a foregone alternative.
A)Opportunity cost
B)Time value of money
C)Inflation
D)An annuity

Accepted Answer

Opportunity cost is the cost of a foregone alternative. It refers to the cost of the next best alternative when making a decision. For example, if you decide to invest in stocks, the opportunity cost would be the return you could have earned if you had invested in bonds or real estate instead.

Question 20

Eastinghome Inc.just paid $8,000 to a landowner to explore for but not extract valuable minerals.If the landowner invests the money at a rate of 5.5% compounded annually for 7 years what is the investment worth at the end of that time period?
A)$5,499.49
B)$11,637.43
C)$56,000.00
D)$66,135.15

Accepted Answer

The investment's future value can be calculated using the formula for compound interest: $FV = P(1 + r)^n$, where $FV$ is the future value, $P$ is the principal amount ($8,000), $r$ is the annual interest rate (5.5% or 0.055), and $n$ is the number of years (7). Plugging in the values: $FV = 8000(1 + 0.055)^7$, which calculates to approximately $11,637.43.

Quiz 7: Time Value of Money Basics and Applications

You own a contract that promises an annuity cash flow of $100 beginning-of-the-year cash flows for each of the next three years (note: the first cash flow is today) .At an interest rate of 10%,what is the future value of this contract exactly three years from today?

Your parents paid $1,000 for a college fund bond when you were born.Today is your 20^th birthday and you are ready to cash the bond which has grown to a value of $3,361.85.What was the average annual rate of return on your college fund bond?

You own a contract that promises an annuity cash flow of $100 beginning-of-the-year cash flows for each of the next three years (note: the first cash flow is today) .At an interest rate of 10%,what is the present value of this contract?

Individuals and businesses require compensation for delaying consumption.Which of the following questions may contribute to the magnitude of the compensation?

Your friend has agreed to lend you $5,000 today if you will repay him $5,061.36 in three months.What annual interest rate is your friend charging you for this loan?

Peabody Books Inc.wishes to borrow $182,000 today for the purchase of publishing materials.They have an agreement with their commercial banker that they can borrow money at an annual rate of 4.75%.How much will the firm owe if they repay the loan in exactly one year?

What is the present value of $3,500 received 3 years from today if the prevailing interest rate is 6.10%?

You own a contract that promises an annuity cash flow of $100 year-end cash flows for each of the next three years (note: the first cash flow is exactly one year from today) .At an interest rate of 10%,what is the present value of this contract?

Which choice has a greater present value if we assume a required rate of return of 10%? 1: A lump sum cash flow today of $248.69,2: $100 cash flows occurring one,two,and three years from today,or 3: a single cash flow of $331 three years from today.

Consider the equation for present value.If you wished to increase the present value of a future amount by changing only one variable,which of the following actions should you take?

Autorola plans to invest money today at an interest rate of 6% compounded annually to have $40,000 available for the purchase of a car four years from now.How much does the firm need to invest today?

If you were able to invest $2,500 at a rate of 6.40% for six months,how much money would you have at the end of that period?

You have decided to endow a Chair in Finance at Whatsamatta University.How much money must you deposit into the endowment account today if the Chair pays $125,000 per year forever (first payment one year from today) and is invested at a rate that pays out 4.50% per year?

________ is the cost of a foregone alternative.

Eastinghome Inc.just paid $8,000 to a landowner to explore for but not extract valuable minerals.If the landowner invests the money at a rate of 5.5% compounded annually for 7 years what is the investment worth at the end of that time period?