Question 1

Which of the following statements is correct?
A) $100 to be received in the future is worth more than that today since it could be invested and earn interest.
B) $100 to be received in the future is worth less than that today since it could be invested and earn interest.
C) The Rule of 72 calculates the compounded return on investments.
D) Discounting is finding the future value of an original investment.

Accepted Answer

$100 to be received in the future is worth less than that today due to the potential of current funds to be invested and earn interest, a concept known as the time value of money.

Question 2

Five years ago, sales were $4 million. Today your company's sales are $10 million. What annual rate have sales been growing?
A) 1.5%
B) 12.65%
C) 16.65%
D) 20.11%

Accepted Answer

The answer of Five years ago, sales were $4 million....

Question 3

Assume you borrow $500 from a payday lender. The terms are that you must pay a fee of $75 in advance (today) and one year from now you need to repay $750. What implied interest rate are you paying?
A) 43.09%
B) 55.78%
C) 76.47%
D) 81.03%

Accepted Answer

The answer of Assume you borrow $500 from a payday...

Question 4

Which of the following investments would you prefer?
A) An investment earning 10% for 20 years
B) An investment earning 8.5% for 20 years
C) An investment earning 5% for 40 years
D) An investment earning 3% for 40 years

Accepted Answer

The answer of Which of the following investments would you...

Question 5

When your investment compounds, your money will grow in a(n) __________ fashion.
A) linear
B) exponential
C) static
D) implied

Accepted Answer

When your investment compounds, the interest earned is added back to the principal amount, which then earns a return on the increased amount. This leads to exponential growth, meaning that the money will grow at a faster and faster rate over time.

Question 6

You have $100,000 in your account. Assuming no additional deposits are made and your account earns 15% per year, how long will it take for the account to have a balance of $500,000?
A) 10.28 years
B) 11.09 years
C) 11.52 years
D) 12.64 years

Accepted Answer

We can use the formula for compound interest to solve this problem:
A = P(1+r/n)^(nt)
where A is the ending balance, P is the starting balance, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:
500,000 = 100,000(1+0.15/1)^(1*t)
5 = (1.15)^t
t = log(5)/log(1.15)
t ≈ 11.52

Therefore, it will take approximately 11.52 years for the account to have a balance of $500,000.

Question 7

A firm's net income last year was $2.65 million. Its net income grew 8% during the last 5 years. If that growth rate continues, how long will it take for the firm's net income to double?
A) 6.6 years
B) 7.1 years
C) 8.2 years
D) 9 years

Accepted Answer

The answer of A firm's net income last year was...

Question 8

Which of the following will not increase a present value?
A) Increase the interest rate.
B) Decrease the number of periods.
C) Increase the future value.
D) None of these answers is correct.

Accepted Answer

The answer of Which of the following will not increase...

Question 9

We call the process of earning interest on both the original deposit and on the earlier interest payments _______________.
A) simple interest
B) compounding
C) future value
D) discounting

Accepted Answer

Compounding refers to the process of earning interest not only on the original deposit but also on the earlier interest payments, thus increasing the total amount of interest earned. Simple interest only earns interest on the original deposit, while future value and discounting are calculation methods used in finance.

Question 10

Suppose a U.S. Treasury bond promises to pay $9,780.13 in three years. If bonds of this type are generating a 4% annual return, how much would you pay for this bond today?
A) $8,429.71
B) $11,001.32
C) $8,694.50
D) $9,112.78

Accepted Answer

The formula to calculate the present value of a bond is:
PV = FV / (1 + r)^n

Where:
PV = Present Value
FV = Future Value
r = Rate of Return
n = number of periods

In this case, FV = $9,780.13, r = 4%, and n = 3 years.

Plugging these values into the formula, we get:
PV = $9,780.13 / (1 + 0.04)^3
PV = $8,694.50

Therefore, the best choice is C, $8,694.50.

Question 11

You want to retire in 25 years and you have just inherited $300,000. You believe you will need $1,450,000 upon retirement. What rate will you need to earn on the account to achieve this goal?
A) 4.5%
B) 5.5%
C) 6.5%
D) 8.5%

Accepted Answer

To determine the needed rate of return, we can use the Future Value formula:

FV = PV * (1 + r)^n

where FV is the future value or desired amount ($1,450,000), PV is the present value ($300,000), r is the rate of return, and n is the number of years (25).

Plugging in the values we have, we get:

$1,450,000 = $300,000 * (1 + r)^25

Simplifying this equation, we get:

(1 + r)^25 = 4.833

Taking the 25th root of both sides, we get:

1 + r = 1.065

Subtracting 1 from both sides, we get the rate of return needed:

r = 0.065, or 6.5%

Therefore, the best choice is C) 6.5%.

Question 12

How long will it take for the purchasing power of $1 to be cut in half if inflation is 4%?
A) 4.97 years
B) 7.42 years
C) 10.72 years
D) 17.67 years

Accepted Answer

The answer of How long will it take for the...

Question 13

Which of the following statements is incorrect with respect to time lines?
A) A helpful tool for organizing our analysis is the time line.
B) Cash flows we receive are called inflows are denoted with a positive number.
C) Cash flows we pay out are called outflows are designated with a negative number.
D) Interest rates are not included on our time lines.

Accepted Answer

Interest rates are typically included on time lines as they impact the time value of money and ultimately the calculation of future cash flows.

Question 14

Which of the following is the equivalent of $300 received today?
A) $795.99 to be received 20 years in the future assuming a 5% annual interest rate.
B) $100 to be received two years from now and $200 three years from now.
C) $300 compounded at 10% for one year.
D) All of these are the equivalent of $300 received today.

Accepted Answer

The present value of $795.99 received in 20 years at a 5% interest rate is $300.

Question 15

You are considering an investment that is expected to pay 5% in year 1, 7% in years 2 and 3 and 9% in year 4. If you invest $2,000 today, what will this investment be worth at the end of the fourth year?
A) $2,501.42
B) $2,693.71
C) $2,713.04
D) $2,620.68

Accepted Answer

The answer of You are considering an investment that is...

Question 16

You borrow $3,500 and will pay back the entire amount in 5 years. You are charged 9% interest per year. How much interest do you pay on this loan?
A) $1,885.18
B) $1,907.35
C) $1,959.02
D) $2,106.81

Accepted Answer

The correct answer is A. The total interest paid on the loan is $1,885.18. This is calculated as follows:Interest = Principal x Rate x TimeInterest = $3,500 x 0.09 x 5Interest = $1,885.18

Question 17

Your firm receives an offer from the supplier who provides computer chips used to manufacture cell phones. Due to poor planning, the supplier has an excess amount of chips and is willing to sell $600,000 worth of chips for only $500,000. You already have two years' supply on hand. It would cost you $7,500 today to store the chips until your firm needs them in two years. What implied interest rate would you be earning if you purchased and store the chips?
A) 6.57%
B) 8.73%
C) 9.54%
D) 18.23%

Accepted Answer

The implied interest rate can be calculated using the formula for the future value of money. The cost today is $500,000 + $7,500 = $507,500, and the future value is $600,000. Using the formula FV = PV * (1 + r)^n, where FV is the future value, PV is the present value, r is the interest rate, and n is the number of periods, we solve for r: $600,000 = $507,500 * (1 + r)^2. Solving for r gives approximately 8.73%.

Question 18

You invested $1000 for 5 years in an account that earns 5%. However, today you learn that you are able to move the account into an investment that earns 10%. Which of the following statements is correct?
A) If you select the investment earning 10%, you will double your profit.
B) If you select the investment earning 10%, you will more than double your profit.
C) If you select the investment earning 10%, your profit will be less than double.
D) None of these statements is correct.

Accepted Answer

If you leave the account in the 5% investment for 5 years, the future value will be:

FV = $1000 * (1 + 0.05)^5
FV = $1,276.28

If you move the account to the 10% investment for the remaining 5 years, the future value will be:

FV = $1,276.28 * (1 + 0.10)^5
FV = $2,078.93

So, the profit from the 5% investment is $276.28 ($1,276.28 - $1000), while the profit from the 10% investment is $1,078.93 ($2,078.93 - $1000). Therefore, if you select the investment earning 10%, you will more than double your profit.

Question 19

A $400 investment has doubled to $800 in six years because of a 12.25% return. How much longer will it take for the investment to reach $1100 if it continues to earn 12.25%?
A) 2.56 years
B) 2.76 years
C) 3.46 years
D) 5 years

Accepted Answer

To solve this problem, we can use the formula for compound interest:

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

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Using the given information, we know that P = 400, A = 1100, r = 0.1225, and n = 1 (compounded yearly). We can solve for t by substituting these values into the formula and solving for t:

1100 = 400(1 + 0.1225/1)^(1t)
2.75 = (1.1225)^t
log(2.75) = t*log(1.1225)
t = log(2.75)/log(1.1225)
t ≈ 2.76 years

Therefore, it will take approximately 2.76 more years for the investment to reach $1100 if it continues to earn 12.25% per year.

Question 20

You double your money in 5 years. The reason your return is not 20% per year is because ___.
A) it is probably a "fad" investment
B) it does not reflect the effect of discounting
C) it does not reflect the effect of the Rule of 72
D) it does not reflect the effect of compounding

Accepted Answer

The reason for doubling your money in 5 years is due to compounding, where your returns from previous years are reinvested and added to your initial investment, allowing for exponential growth. A 20% annual return would not necessarily result in a doubling of money in 5 years due to the effect of compounding. The other options (A, B, C) are not relevant to the explanation of the return.

Quiz 4: Time Value of Money 1: Analyzing Single Cash Flows

Which of the following statements is correct?

Five years ago, sales were $4 million. Today your company's sales are $10 million. What annual rate have sales been growing?

Assume you borrow $500 from a payday lender. The terms are that you must pay a fee of $75 in advance (today) and one year from now you need to repay $750. What implied interest rate are you paying?

Which of the following investments would you prefer?

When your investment compounds, your money will grow in a(n) __________ fashion.

You have $100,000 in your account. Assuming no additional deposits are made and your account earns 15% per year, how long will it take for the account to have a balance of $500,000?

A firm's net income last year was $2.65 million. Its net income grew 8% during the last 5 years. If that growth rate continues, how long will it take for the firm's net income to double?

Which of the following will not increase a present value?

We call the process of earning interest on both the original deposit and on the earlier interest payments _______________.

Suppose a U.S. Treasury bond promises to pay $9,780.13 in three years. If bonds of this type are generating a 4% annual return, how much would you pay for this bond today?

You want to retire in 25 years and you have just inherited $300,000. You believe you will need $1,450,000 upon retirement. What rate will you need to earn on the account to achieve this goal?

How long will it take for the purchasing power of $1 to be cut in half if inflation is 4%?

Which of the following statements is incorrect with respect to time lines?

Which of the following is the equivalent of $300 received today?

You are considering an investment that is expected to pay 5% in year 1, 7% in years 2 and 3 and 9% in year 4. If you invest $2,000 today, what will this investment be worth at the end of the fourth year?

You borrow $3,500 and will pay back the entire amount in 5 years. You are charged 9% interest per year. How much interest do you pay on this loan?

You invested $1000 for 5 years in an account that earns 5%. However, today you learn that you are able to move the account into an investment that earns 10%. Which of the following statements is correct?

A $400 investment has doubled to $800 in six years because of a 12.25% return. How much longer will it take for the investment to reach $1100 if it continues to earn 12.25%?

You double your money in 5 years. The reason your return is not 20% per year is because ___.