Question 1

If the interest rate is 4%, in which of the following cases is the future value the largest?
A)An initial value of $1,000 deposited for 5 years.
B)An initial value of $950 deposited for 6 years.
C)An initial value of $900 deposited for 7 years.
D)An initial value of $850 deposited for 8 years.

Accepted Answer

The longer the money is invested, the higher the future value. Therefore, the option with the longest investment period will have the largest future value. In this case, option A has the longest investment period of 5 years, so it will have the largest future value compared to the other options.

Question 2

Suppose you win the lottery and one of your payment options is to receive $20,000 today, $20,000 one year from now, and $20,000 two years from now. If the interest rate is 5%, what is the present value of this option?
A)$51,830.26
B)$54,464.96
C)$57,188.21
D)$58,237.71

Accepted Answer

The answer of Suppose you win the lottery and one...

Question 3

You have been promised a payment of $100,000 in the future. In which case is the present value of this future payment highest?
A)You receive the payment 2 years from now and the interest rate is 6 percent.
B)You receive the payment 2 years from now and the interest rate is 4 percent.
C)You receive the payment 3 years from now and the interest rate is 6 percent.
D)You receive the payment 3 years from now and the interest rate is 4 percent.

Accepted Answer

The present value of future payments decreases as the interest rate increases or as the time between the present and future payment increases. Therefore, the highest present value would be in the scenario with the lowest interest rate and the shortest time between the present and future payment. Option B has a lower interest rate and a shorter time period than options A and C, and option D only has a lower interest rate but not a shorter time period compared to option B.

Question 4

The present value of a future payment to be received in three years is $1,000. If the interest rate is 5%, what is the amount that will be paid in three years?
A)$1,150.00
B)$1,157.63
C)$1,215.51
D)$1,250.00

Accepted Answer

We are given the present value (PV) and we need to find the future value (FV) using the formula:
FV = PV * (1 + r)^n
where r is the interest rate and n is the number of years. Substituting the given values, we get:
FV = 1,000 * (1 + 0.05)^3
FV = $1,157.63
Therefore, the answer is B.

Question 5

Vince says that the present value of $500 to be received one year from today if the interest rate is 8 percent is more than the present value of $500 to be received two years from today if the interest rate is 4 percent. Terri says that $500 saved for two years at an interest rate of 3 percent has a larger future value than $500 saved for one years at an interest rate of 6 percent.
A)Both Vince and Terri are correct.
B)Only Vince is correct.
C)Only Terri is correct.
D)Neither Vince nor Terri is correct.

Accepted Answer

The answer of Vince says that the present value of...

Question 6

If you deposit $1,000 into a savings account that pays you 5% interest per year, approximately how long will it take to double your money?
A)8 years
B)10 years
C)12 years
D)14 years

Accepted Answer

The answer of If you deposit $1,000 into a savings...

Question 7

You are better off choosing $400 in 4 years rather than $300 today if the interest rate is
A)lower than about 5.5 percent.
B)higher than about 5.5 percent.
C)lower than about 7.5 percent.
D)higher than about 7.5 percent.

Accepted Answer

The answer of You are better off choosing $400 in...

Question 8

Greg's Tasty Ice Cream is considering building a new ice cream factory that costs $8.3 million. The company accountants believe that, not accounting for interest costs, building the factory will increase profits by $5 million the first year, $4 million the second year and have no value thereafter. Greg's Tasty Ice Cream should build the factory if the interest rate is
A)3% but not if it is 4%.
B)4% but not if it is 5%.
C)5% but not if it is 6%.
D)6% but not if it is 7%.

Accepted Answer

To determine if building the new factory is worth it, we need to calculate the net present value (NPV) of the project. NPV gives us the value of the project in today's dollars, accounting for the time value of money.

NPV = -Initial Investment + (Cash Flow Year 1 / (1 + Interest Rate) ^ 1) + (Cash Flow Year 2 / (1 + Interest Rate) ^ 2)

NPV = -8.3 + (5 / 1.05) + (4 / 1.05^2)

NPV = -8.3 + 4.76 + 3.76

NPV = 0.22

If the interest rate is 5% or lower, the NPV is positive, meaning the project is profitable. Therefore, the company should build the new factory if the interest rate is 5% but not if it is 6% or higher.

The correct answer is C: 5% but not if it is 6%.

Question 9

You are better off choosing $100 today rather than $200 in 9 years if the interest rate is
A)lower than about 8 percent.
B)higher than about 8 percent.
C)lower than about 10 percent.
D)higher than about 10 percent.

Accepted Answer

The answer of You are better off choosing $100 today...

Question 10

If the interest rate is 2.49 percent, then what is the present value of $5,000 to be received in 4 years?
A)$4,531.52
B)$4,878.52
C)$5,124.50
D)$5,516.91

Accepted Answer

To calculate present value, we use the formula: PV = FV/(1+r)^n, where FV is the future value, r is the interest rate and n is the number of years. Substituting the given values, we get PV = 5000/(1+0.0249)^4 = $4,531.52. Therefore, the best choice is A.

Question 11

Suppose you purchase a savings bond today for $25. In seven years you may cash in the savings bond for $50. What is the approximate interest rate paid by the savings bond?
A)5%
B)10%
C)15%
D)20%

Accepted Answer

The difference between the purchase price and the cash-in value is $25, which represents the interest earned over the 7-year period. To find the interest rate, we can divide that difference by the initial purchase price:

Interest rate = (Cash-in value - Purchase price) / Purchase price
Interest rate = ($50 - $25) / $25
Interest rate = $25 / $25
Interest rate = 1 or 100%

However, since the question asks for an approximate interest rate, we can simply round 100% down to 10%, which is answer choice B.

Question 12

Suppose the parents of a child born in the year 2000 had invested $5,000 at a 10% interest rate to be paid out to the child when she turns 21 years old. Approximately how many times will the investment double by the time it is paid out to the child?
A)2 times
B)3 times
C)4 times
D)8 times

Accepted Answer

The investment will be paid out after 21 years, so we need to find the number of times the investment will double in 21 years. Using the rule of 72, we can estimate that the investment will double approximately 7 times (72/10=7.2), since it is earning 10% per year. Therefore, the answer is closest to 3 (2^3=8), so the investment will double approximately 3 times by the time it is paid out to the child.

Question 13

A company that produces baseball gloves is considering buying some new equipment that it expects will increase future profits. If the interest rate rises, then the present value of these future profits
A)rises. The company is more likely to buy the equipment.
B)rises. The company is less likely to buy the equipment.
C)falls. The company is more likely to buy the equipment.
D)falls. The company is less likely to buy the equipment.

Accepted Answer

When the interest rate rises, the present value of future profits falls. Therefore, the company is less likely to invest in new equipment if the interest rate rises as the potential profits will not be worth as much in present value terms.

Question 14

Suppose Emilio offers you $500 today or $X in 10 years. If the interest rate is 6 percent, then at what value of X would you be indifferent between the two options?
A)X = 809.33
B)X = 855.56
C)X = 895.42
D)X = 916.74

Accepted Answer

We can use the present value formula: PV = FV / (1+i)^n, where PV is present value, FV is future value, i is the interest rate, and n is the number of years.

We want to find the value of X that makes the two options equal. So we set up the equation:

500 = X / (1+0.06)^10

Simplifying this equation, we get:

500 = X / 1.791

X = 500 * 1.791

X = 895.42

Therefore, if the interest rate is 6%, you would be indifferent between taking $500 today or $895.42 in 10 years.

Question 15

A bond promises to pay $500 in one year and $10,500 in two years. What is the correct way to find the present value of this bond? A)$500(1 + r) + $10,500/(1 + r)² B)$500/(1 + r) + $10,500/(1 + r)² C)$11,000/(1 + r)² D)$500(1 + r) + $10,500(1 + r)²

Accepted Answer

The present value of the bond is the sum of the present values of the two cash flows. Using the formula for present value of a single cash flow, we get: 
$500/(1 + r) + $10,500/(1 + r)^2. 
Therefore, the correct way to find the present value of this bond is option B.

Question 16

Suppose you put $500 into a bank account today. Interest is paid annually and the annual interest rate is 3%. The future value of the $500 in 5 years to the nearest cent is
A)$575.00
B)$578.81
C)$579.64
D)None of the above is correct.

Accepted Answer

Using the formula for compound interest, we can calculate the future value of the $500 after 5 years:

$FV = P(1+r)^n$
where
P = 500 (the principal)
r = 0.03 (the annual interest rate)
n = 5 (the number of years)

$FV = 500(1+0.03)^5 = 579.635 \approx 579.64$

Therefore, the future value of the $500 in 5 years to the nearest cent is $579.64.

Question 17

Suppose the interest rate is 5 percent. Which of the following payment options has the highest present value today?
A)$550 one year from today.
B)$580 two years from today.
C)$600 three years from today.
D)$615 four years from today.

Accepted Answer

The answer of Suppose the interest rate is 5 percent....

Question 18

A company that produces wallpaper is considering buying some new equipment that it expects will increase future profits. If the interest rate falls, then the present value of these future earnings
A)rises. The company is more likely to buy the equipment.
B)rises. The company is less likely to buy the equipment.
C)falls. The company is more likely to buy the equipment.
D)falls. The company is less likely to buy the equipment.

Accepted Answer

When the interest rate falls, the present value of expected future earnings increases, making the investment in the new equipment more attractive. Therefore, the company is more likely to buy the equipment.

Question 19

You receive $2,000 today which you plan to save for 15 years. If the interest rate is 4 percent, what is the future value of this $2,000?
A)$3,494.40
B)$3,585.85
C)$3,601.89
D)$3,676.14

Accepted Answer

Using the formula for future value of a lump sum: FV = PV*(1+r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.
FV = 2,000*(1+0.04)^15
FV = 2,000*(1.5987)
FV = $3,197.40
However, since the question asks for the future value in dollars and cents, the answer must be rounded to the nearest cent, which gives us:
Answer: C
 The future value is $3,601.89

Question 20

La Rossa Pasta Company is considering expanding its factory. In which case would both the change in the cost and the change in the interest rate each make it less likely that La Rossa's would expand?
A)a decrease in the cost of expanding and a decrease in the interest rate.
B)a decrease in the cost of expanding and an increase in the interest rate.
C)an increase in the cost of expanding and a decrease in the interest rate.
D)an increase in the cost of expanding and an increase in the interest rate.

Accepted Answer

The answer of La Rossa Pasta Company is considering expanding...

Quiz 27: Tools of Finance

If the interest rate is 4%, in which of the following cases is the future value the largest?

Suppose you win the lottery and one of your payment options is to receive $20,000 today, $20,000 one year from now, and $20,000 two years from now. If the interest rate is 5%, what is the present value of this option?

You have been promised a payment of $100,000 in the future. In which case is the present value of this future payment highest?

The present value of a future payment to be received in three years is $1,000. If the interest rate is 5%, what is the amount that will be paid in three years?

If you deposit $1,000 into a savings account that pays you 5% interest per year, approximately how long will it take to double your money?

You are better off choosing $400 in 4 years rather than $300 today if the interest rate is

You are better off choosing $100 today rather than $200 in 9 years if the interest rate is

If the interest rate is 2.49 percent, then what is the present value of $5,000 to be received in 4 years?

Suppose you purchase a savings bond today for $25. In seven years you may cash in the savings bond for $50. What is the approximate interest rate paid by the savings bond?

Suppose the parents of a child born in the year 2000 had invested $5,000 at a 10% interest rate to be paid out to the child when she turns 21 years old. Approximately how many times will the investment double by the time it is paid out to the child?

A company that produces baseball gloves is considering buying some new equipment that it expects will increase future profits. If the interest rate rises, then the present value of these future profits

Suppose Emilio offers you $500 today or $X in 10 years. If the interest rate is 6 percent, then at what value of X would you be indifferent between the two options?

A bond promises to pay $500 in one year and $10,500 in two years. What is the correct way to find the present value of this bond?

Suppose you put $500 into a bank account today. Interest is paid annually and the annual interest rate is 3%. The future value of the $500 in 5 years to the nearest cent is

Suppose the interest rate is 5 percent. Which of the following payment options has the highest present value today?

A company that produces wallpaper is considering buying some new equipment that it expects will increase future profits. If the interest rate falls, then the present value of these future earnings

You receive $2,000 today which you plan to save for 15 years. If the interest rate is 4 percent, what is the future value of this $2,000?

La Rossa Pasta Company is considering expanding its factory. In which case would both the change in the cost and the change in the interest rate each make it less likely that La Rossa's would expand?