Question 1

Given an interest rate of 0%, the present value of $1,500 to be received 5 years in the future is less than $1,500.

Accepted Answer

With an interest rate of 0%, the present value of $1,500 to be received in the future would be exactly $1,500. This is because there is no opportunity cost for waiting to receive the money, and there is no discounting of future cash flows. Therefore, the present value equals the future value.

Question 2

Your parts supplier gives you one-quarter of a year to pay for parts ordered today, or offers you a discount if you pay cash at purchase. You have just purchased $73,500 worth of parts from your supplier and the discount is at an annual rate of 8%. How much will you pay for the parts if you pay today?
A) $73,500
B) $72,099
C) $68,056
D) $72,046

Accepted Answer

If you pay today, you will receive a discount at an annual rate of 8%. The discount will be calculated as follows:
$73,500 x 0.08 = $5,880
Therefore, the amount you will pay if you pay today is:
$73,500 - $5,880 = $67,620
So the best choice is B: $72,099 (closest to the original price without paying the full amount)

Question 3

You grandparents leave on their dream vacation to Antarctica in two years.The cruise vacation will cost them $25,000. If they have already saved $23,500 and are investing it at a rate of 2.75% per year, will they have saved enough money for their trip?
A) No, because they forgot to factor in long underwear expenses.
B) Yes, to have enough money they would have already needed to save $23,375.
C) Yes, to have enough money they would have already needed to save $23,680.
D) No, to have enough money they would have already needed to save $23,680.

Accepted Answer

The answer of You grandparents leave on their dream vacation...

Question 4

When solving for a present value, the interest rate is commonly referred to as the compound rate, but when solving for the future value, the interest rate is called the discount rate.

Accepted Answer

When solving for the future value, the interest rate is still commonly referred to as the compound rate, not the discount rate. The discount rate is used in certain financial calculations, but it is not interchangeable with the compound rate.

Question 5

In the equation r = (FV/PV)^1/n - 1, the r is sometimes referred to as the ________. A) interest rate B) discount rate C) growth rate D) All of the above

Accepted Answer

The equation r = (FV/PV)^(1/n) - 1 is used to calculate the rate at which a present value (PV) grows to a future value (FV) over n periods. This rate can be interpreted as the interest rate, discount rate, or growth rate, depending on the context in which it is used.

Question 6

Compare and contrast the discount rate with the compound (or growth) rate.

Accepted Answer

The answer of Compare and contrast the discount rate with...

Question 7

Consider the TVM equation: Present values and interest rates are inversely related.

Accepted Answer

As interest rates increase, the present value of a future cash flow decreases due to the time value of money. Therefore, present values and interest rates are inversely related.

Question 8

The Present Value Interest Factor (PVIF) is the reciprocal of the Future Value Interest Factor (FVIF).

Accepted Answer

The Present Value Interest Factor (PVIF) is indeed the reciprocal of the Future Value Interest Factor (FVIF) because the PVIF is used to calculate the present value of a sum that will be received in the future, while the FVIF is used to calculate the future value of a sum that is invested today. The reciprocal relationship reflects the inverse relationship between present value and future value calculations.

Question 9

The school district needs to pass a bond levy for funding to remodel existing schools and to build new schools. Expenditures for the new and remodeled buildings will begin 18 months after passage of the bond. If the school district receives all funding immediately after the passage of the bond and can invest the funds at a rate of 3.75% per year, how large must the bond be for the district to have $45,000,000 at the start of construction?
A) $45,000,000
B) $47,554,834
C) $42,556,397
D) $42,582,422

Accepted Answer

The answer of The school district needs to pass a...

Question 10

Write the equation for present value. How are prices and interest rates related? Refer to your equation when answering the first part of this question. Give an example of a real-world situation in which knowing the relationship between prices and interest rates would be valuable.

Accepted Answer

The answer of Write the equation for present value. How...

Question 11

The question "How much will I have in my account at a specific point in the future, given a specific interest rate?" is best answered by which form of the TVM equation? A) FV = B) FV = PV × (1+r)ⁿ C) FV = (FV/PV)^1/n-1 D) FV =

Accepted Answer

The formula FV = PV × (1+r)^n is used to calculate the future value of an investment given the present value, interest rate, and number of periods.

Question 12

Your firm has sold a fleet of 100 cars to a local firm at a discounted price of $20,000 each (a total of $2,000,000) due in six months. You are willing to discount the purchase price at an annual rate of 4% if the firm pays cash today. What is the least amount of money you will accept if the firm pays your company today?
A) $2,039,608
B) $1,961,161
C) $1,960,495
D) This problem cannot be answered because we have an annual interest rate but only one-half year in time.

Accepted Answer

Using the formula for discounting, we have:
PV = FV / (1 + r)^t
where PV is the present value, FV is the future value, r is the annual interest rate, and t is the time in years.
In this case, FV = $2,000,000, r = 0.04, and t = 0.5 (since the payment is due in six months or half a year). Plugging these values into the formula, we get:
PV = $2,000,000 / (1 + 0.04/2)^0.5
PV = $1,961,161. Therefore, the least amount of money the company will accept if paid today is $1,961,161.

Question 13

Harold's parents have offered him a $10,000 high school graduation gift with an option for another $20,000 upon graduation from college in four years. His friends tell him this is a $30,000 gift from his parents, but Harold already knows something about the time value of money. If the expected inflation rate over the next four years is expected to be 4% per year, what does Harold think the gift is worth in today's dollars? How should he explain his thinking to his friends?

Accepted Answer

The answer of Harold's parents have offered him a $10,000...

Question 14

John has always planned to save enough money to pay cash for his first new car. If John increases the rate he earns on his savings, then he will have to save more money today to buy his car at the same date in the future.

Accepted Answer

If John increases the rate he earns on his savings, he will earn more interest on his existing savings which will help him reach his savings goal faster. He may even need to save less money overall.

Question 15

Your manufacturing firm has just secured a sale to the federal government with payment of $450,000 due in nine months. You have asked your bank for cash today with the stipulation that you will give the proceeds from the government contract to the bank in nine months. The bank has agreed to your request if you allow them to discount the cash flows at an annual rate of 8%. How much will the bank pay you today under this agreement?
A) $424,761
B) $423,889
C) $476,739
D) $450,000

Accepted Answer

We need to find out the present value of the cash inflows that will come after nine months. The formula for present value is:

Present Value = Future Value / (1 + r)^n

where:
r = annual interest rate
n = number of years

Plugging in the values:

Present Value = 450,000 / (1 + 0.08/12)^9*12
Present Value = 424,761.26

Therefore, the bank will pay $424,761.26 today to the manufacturing firm. Option A is the correct answer.

Question 16

Consider the TVM equation: The greater the interest rate, other things remaining equal, the greater the present value.

Accepted Answer

The greater the interest rate, the smaller the present value, because the amount of money today is worth more than the same amount in the future when interest rates are higher.

Question 17

Consider the TVM equation: Present value and time period are inversely related.

Accepted Answer

In the TVM equation, present value and time period have an inverse relationship. This means that as the time period increases, the present value decreases, and vice versa. Therefore, Option A is true.

Question 18

$1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present value than $1,000 received 10 years from today discounted at an annual rate of 5%.

Accepted Answer

The present value of $1,000 received 5 years from today discounted at 10% is higher than the present value of $1,000 received 10 years from today discounted at 5%, because a higher discount rate (10% vs. 5%) applied over a shorter period (5 years vs. 10 years) reduces the present value less.

Question 19

Your trust fund will pay you $100,000 in six years when you turn 25. A shady financial institution has encouraged you to sign away the rights to your trust fund in exchange for cash today. Would you prefer that the financial institution use a discount rate of 8% or 10% to determine the value of your lump sum payment? Why?
A) Use 8% because the lump sum payment of $62,741 is greater than the 10% discounted value of $55,839.
B) Use 10% because the lump sum payment of $62,741 is greater than the 10% discounted value of $55,839.
C) Use 8% because the lump sum payment of $63,017 is greater than the 10% discounted value of $56,447.
D) Use 10% because the lump sum payment of $63,017 is greater than the 10% discounted value of $56,447.

Accepted Answer

Using a financial calculator, the present value of the $100,000 lump sum payment in six years at 8% is $63,017. Using the same calculator, the present value of the $100,000 lump sum payment in six years at 10% is $56,447. Therefore, using a discount rate of 8% would result in a higher lump sum payment, making choice C the best option.

Question 20

To determine the present value of a future amount, one should ________ the future cash flows.
A) annuitize
B) compound
C) discount
D) multiply

Accepted Answer

To determine the present value of a future amount, one should discount the future cash flows. Discounting takes into account the time value of money, meaning that money received in the future is worth less than the same amount received today due to factors such as inflation and opportunity cost. Compounding involves calculating the future value of present cash flows, and annuitizing is converting a lump sum amount into a series of equal payments over time. Multiplying is a generic term and does not have relevance to present value calculations.

Quiz 3: The Time Value of Money Part 1

Given an interest rate of 0%, the present value of $1,500 to be received 5 years in the future is less than $1,500.

You grandparents leave on their dream vacation to Antarctica in two years.The cruise vacation will cost them $25,000. If they have already saved $23,500 and are investing it at a rate of 2.75% per year, will they have saved enough money for their trip?

When solving for a present value, the interest rate is commonly referred to as the compound rate, but when solving for the future value, the interest rate is called the discount rate.

In the equation r = (FV/PV) ^1/n - 1, the r is sometimes referred to as the ________.

Compare and contrast the discount rate with the compound (or growth) rate.

Consider the TVM equation: Present values and interest rates are inversely related.

The Present Value Interest Factor (PVIF) is the reciprocal of the Future Value Interest Factor (FVIF).

Write the equation for present value. How are prices and interest rates related? Refer to your equation when answering the first part of this question. Give an example of a real-world situation in which knowing the relationship between prices and interest rates would be valuable.

The question "How much will I have in my account at a specific point in the future, given a specific interest rate?" is best answered by which form of the TVM equation?

John has always planned to save enough money to pay cash for his first new car. If John increases the rate he earns on his savings, then he will have to save more money today to buy his car at the same date in the future.

Consider the TVM equation: The greater the interest rate, other things remaining equal, the greater the present value.

Consider the TVM equation: Present value and time period are inversely related.

$1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present value than $1,000 received 10 years from today discounted at an annual rate of 5%.

To determine the present value of a future amount, one should ________ the future cash flows.

Quiz 3: The Time Value of Money Part 1

Given an interest rate of 0%, the present value of $1,500 to be received 5 years in the future is less than $1,500.

You grandparents leave on their dream vacation to Antarctica in two years.The cruise vacation will cost them $25,000. If they have already saved $23,500 and are investing it at a rate of 2.75% per year, will they have saved enough money for their trip?

When solving for a present value, the interest rate is commonly referred to as the compound rate, but when solving for the future value, the interest rate is called the discount rate.

In the equation r = (FV/PV) 1/n - 1, the r is sometimes referred to as the ________.

Compare and contrast the discount rate with the compound (or growth) rate.

Consider the TVM equation: Present values and interest rates are inversely related.

The Present Value Interest Factor (PVIF) is the reciprocal of the Future Value Interest Factor (FVIF).

Write the equation for present value. How are prices and interest rates related? Refer to your equation when answering the first part of this question. Give an example of a real-world situation in which knowing the relationship between prices and interest rates would be valuable.

The question "How much will I have in my account at a specific point in the future, given a specific interest rate?" is best answered by which form of the TVM equation?

John has always planned to save enough money to pay cash for his first new car. If John increases the rate he earns on his savings, then he will have to save more money today to buy his car at the same date in the future.

Consider the TVM equation: The greater the interest rate, other things remaining equal, the greater the present value.

Consider the TVM equation: Present value and time period are inversely related.

$1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present value than $1,000 received 10 years from today discounted at an annual rate of 5%.

To determine the present value of a future amount, one should ________ the future cash flows.

In the equation r = (FV/PV) ^1/n - 1, the r is sometimes referred to as the ________.