Question 1

Melissa offers you $1,000 today or $1,500 in 5 years.You would prefer to take the $1,500 in 5 years if the interest rate is
A)8 percent.
B)9 percent.
C)10 percent.
D)All of the above are correct.

Accepted Answer

If the interest rate is 8 percent, the present value of $1,500 in 5 years is approximately $1,020. This is higher than $1,000 today, making it preferable to wait for the $1,500.

Question 2

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 8 percent.The future value of the $500 after 2 years is
A)$428.67.
B)$470.00.
C)$580.00.
D)$583.20.

Accepted Answer

The future value (FV) of the $500 after 2 years can be calculated using the formula:

FV = PV x (1 + r)^n

where PV is the present value (or initial investment), r is the interest rate per period, and n is the number of periods.

In this case, PV = $500, r = 8% (or 0.08), and n = 2 years.

Thus, FV = $500 x (1 + 0.08)^2 = $500 x 1.1664 = $583.20

Therefore, the best choice is D.

Question 3

Suppose you will receive $500 at some point in the future.If the annual interest rate is 7.5 percent,then the present value of the $500 is
A)$411.26 if the $500 is to be received in 5 years and $338.95 if the $500 is to be received in 10 years.
B)$348.28 if the $500 is to be received in 5 years and $242.60 if the $500 is to be received in 10 years.
C)$291.11 if the $500 is to be received in 5 years and $272.89 if the $500 is to be received in 10 years.
D)$291.11 if the $500 is to be received in 5 years and $236.49 if the $500 is to be received in 10 years.

Accepted Answer

The present value (PV) of receiving $500 in the future can be calculated using the formula PV = FV/(1+r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years in the future.

For receiving $500 in 5 years:
PV = 500/(1+0.075)^5 = $348.28

For receiving $500 in 10 years:
PV = 500/(1+0.075)^10 = $242.60

Therefore, the best choice is B, as it matches the above calculations.

Question 4

Suppose the interest rate is 10 percent.Which of the following payments has the largest present value?
A)You receive $90.91 two years from today.
B)You receive $82.64 one year from today.
C)You receive $75.13 today.
D)All of these payments have the same present value to the nearest cent.

Accepted Answer

The answer of Suppose the interest rate is 10 percent.Which...

Question 5

Discounting refers directly to
A)finding the present value of a future sum of money.
B)finding the future value of a present sum of money.
C)calculations that ignore the phenomenon of compounding for the sake of ease and simplicity.
D)decreases in interest rates over time,while compounding refers to increases in interest rates over time.

Accepted Answer

Discounting involves finding the present value of a future sum of money by applying a discount rate (usually an interest rate). It involves factoring in the time value of money, as money received in the future is worth less than the same amount received today due to inflation and other factors.

Question 6

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 5.5 percent.The future value of the $500 is
A)$637.50 after 5 years and $822.09 after 10 years.
B)$637.50 after 5 years and $775.00 after 10 years.
C)$653.48 after 5 years and $854.07 after 10 years.
D)$688.36 after 5 years and $915.56 after 10 years.

Accepted Answer

The formula to calculate the future value of an investment with annual compounding interest is:
FV = P(1 + r)^n
Where 
FV = Future Value
P = Principal (the initial investment amount)
r = annual interest rate (in decimal form)
n = number of years

Using this formula, we can calculate the future value of $500 after 5 years as:
FV = $500(1 + 0.055)^5 = $653.48

Similarly, the future value after 10 years can be calculated as:
FV = $500(1 + 0.055)^10 = $854.07

Hence, the best choice is C.

Question 7

One way to characterize the difference between compounding and discounting is to say that
A)compounding involves the assumption that the interest rate is zero,whereas discounting does not involve that assumption.
B)discounting involves the assumption that the interest rate is zero,whereas compounding does not involve that assumption.
C)the process of compounding produces a future value,whereas the process of discounting produces a present value.
D)the process of compounding produces a present value,whereas the process of discounting produces a future value.

Accepted Answer

Compounding involves calculating the future value of an amount of money by applying interest over time, while discounting involves calculating the present value of an amount of money by reducing its future value to its worth today. Therefore, compounding produces a future value, whereas discounting produces a present value. Option A and Option B are incorrect as both involve incorrect assumptions about the interest rate. Option D is incorrect as it erroneously reverses the processes of compounding and discounting.

Question 8

James offers you $1,000 today or $X in 7 years.If the interest rate is 4.5 percent,then you would prefer to take the $1,000 today if and only if
A)X < 1,045.00.
B)X < 1,188.89.
C)X < 1,266.67.
D)X < 1,360.86.

Accepted Answer

The future value of $1,000 today at an interest rate of 4.5% compounded annually for 7 years is $1,360.86. You would prefer the $1,000 today if $X in 7 years is less than this amount.

Question 9

If the interest rate is 4 percent,then you would be equally happy if you received a gift of either $100 today or a gift of
A)$110.00 two years from today.
B)$112.49 three years from today.
C)$116.00 four years from today.
D)$123.67 five years from today.

Accepted Answer

We can use the formula for present value with compound interest to compare the present values of each option. The formula is: 
PV = FV/(1+r)^n 
where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. 
For option A, the present value is: 
PV = 100/(1+0.04)^2 = 92.59 
For option B, the present value is: 
PV = 112.49/(1+0.04)^3 = 97.56 
For option C, the present value is: 
PV = 116/(1+0.04)^4 = 97.09 
For option D, the present value is: 
PV = 123.67/(1+0.04)^5 = 97.20 
Therefore, option B has the highest present value and is the best choice.

Question 10

If the interest rate is 7.5 percent,then what is the present value of $4,000 to be received in 6 years?
A)$2,420.68
B)$2,591.85
C)$2,996.33
D)$3,040.63

Accepted Answer

We can use the formula for present value of a single sum: PV = FV/(1+r)^n
PV = 4000/(1+0.075)^6
PV = 4000/1.575818...
PV = $2,591.85 (rounded to nearest cent)
Therefore, the best choice is B.

Question 11

Imagine that someone offers you $X today or $1,500 in 5 years.If the interest rate is 4 percent,then you would prefer to take the $X today if and only if
A)X > 1,055.56.
B)X > 1,120.89.
C)X > 1,232.89.
D)X > 1,338.26.

Accepted Answer

The present value of $1,500 in 5 years at a 4% interest rate is calculated using the formula PV = FV / (1 + r)^n. Plugging in the values, PV = 1500 / (1.04)^5 = 1,232.89. You would prefer $X today if it is greater than this present value.

Question 12

A manufacturing company is thinking about building a new factory.The factory,if built,will yield the company $300 million in 7 years,and it would cost $220 million today to build.The company will decide to build the factory if the interest rate is
A)no less than 4.53 percent.
B)no greater than 4.53 percent.
C)no less than 5.81 percent.
D)no greater than 5.81 percent.

Accepted Answer

To decide whether it is profitable to build the factory, the company needs to calculate the present value of the future revenue minus the cost of building the factory. The calculation is as follows:

PV = (300 million / (1 + r)^7) - 220 million

where r is the interest rate.

To determine the interest rate that makes the PV equal to zero (i.e., the break-even point), we can solve for r:

0 = (300 million / (1 + r)^7) - 220 million

(1 + r)^7 = 300/220

1 + r = (300/220)^(1/7)

1 + r = 1.0453

r = 0.0453 or 4.53%

Therefore, the company will decide to build the factory if the interest rate is no greater than 4.53%. Any interest rate lower than 4.53% will make the project even more profitable.

The answer is therefore B: no greater than 4.53 percent.

Question 13

Suppose you are deciding whether or not to buy a particular bond for $5,980.17.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $10,000.You will buy the bond today if the interest rate is
A)no less than 9.48 percent.
B)no greater than 9.48 percent.
C)no less than 10.83 percent.
D)no greater than 10.83 percent.

Accepted Answer

The answer of Suppose you are deciding whether or not...

Question 14

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 3 percent.The future value of the $500 after 1 year is
A)$485.44.
B)$496.50.
C)$509.28.
D)$515.00.

Accepted Answer

The answer of Suppose you put $500 into a bank...

Question 15

Compounding refers directly to
A)finding the present value of a future sum of money.
B)finding the future value of a present sum of money.
C)changes in the interest rate over time on a bank account or a similar savings vehicle.
D)interest being earned on previously-earned interest.

Accepted Answer

Compounding refers to interest being earned on previously-earned interest. It is the process of adding interest to the principal amount, which results in earning interest on the interest. This can occur in a savings account, investment account, or loan.

Question 16

In which of the following instances is the present value of the future payment the largest?
A)You will receive $1,000 in 5 years and the annual interest rate is 5 percent.
B)You will receive $1,000 in 10 years and the annual interest rate is 3 percent.
C)You will receive $2,000 in 10 years and the annual interest rate is 10 percent.
D)You will receive $2,400 in 15 years and the annual interest rate is 8 percent.

Accepted Answer

The present value of the future payment is largest when the interest rate is higher and the time to receive the payment is shorter. Therefore, option A is the best choice as it has a higher interest rate and shorter time frame than the other options.

Question 17

Suppose your uncle offers you $100 today or $150 in 10 years.You would prefer to take the $100 today if the interest rate is
A)3 percent.
B)4 percent.
C)5 percent.
D)None of the above is correct.

Accepted Answer

If the interest rate is 5 percent, the future value of $100 today in 10 years would be $162.89, which is more than $150. Therefore, you would prefer to take the $100 today.

Question 18

Imagine that someone offers you $100 today or $200 in 10 years.You would prefer to take the $100 today if the interest rate is
A)4 percent.
B)6 percent.
C)8 percent.
D)All of the above are correct.

Accepted Answer

At an 8 percent interest rate, the future value of $100 today would exceed $200 in 10 years, making it more beneficial to take the $100 now.

Question 19

Suppose you put $350 into a bank account today.Interest is paid annually and the annual interest rate is 6 percent.The future value of the $350 after 4 years is
A)$414.09.
B)$434.00.
C)$441.87.
D)$481.24.

Accepted Answer

To calculate the future value of a single sum investment, we use the formula:

FV = PV x (1 + r)^n

FV = future value 
PV = present value 
r = annual interest rate 
n = number of years

Plugging in the values, we get:

FV = 350 x (1 + 0.06)^4 
FV = 350 x 1.262476 
FV = $441.87

Therefore, the best choice is C.

Question 20

Suppose you are deciding whether to buy a particular bond.If you buy the bond and hold it for 4 years,then at that time you will receive a payment of $10,000.If the interest rate is 6 percent,you will buy the bond if its price today is no greater than
A)$8,225.06.
B)$7,920.94.
C)$7,672.58.
D)$6,998.98.

Accepted Answer

To calculate the maximum price we are willing to pay for the bond, we need to discount the $10,000 payment back to the present using the 6% interest rate. The formula for calculating the present value of a future payment is:

Present value = Future value / (1 + interest rate)^n

where n is the number of years until the payment is received.

In this case, n = 4 and the future value is $10,000. Plugging in the values, we get:

Present value = $10,000 / (1 + 0.06)^4 = $7,920.94

Therefore, if the bond is priced at $7,920.94 or lower, we should buy it, because we will still receive a positive return after taking into account the interest rate. Any higher price would result in a negative return. Among the given choices, option B is the closest to this maximum price, so it is the best choice.

Quiz 14: The Basic Tools of Finance: Present Value Measuring the Time Value of Money

Melissa offers you $1,000 today or $1,500 in 5 years.You would prefer to take the $1,500 in 5 years if the interest rate is

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 8 percent.The future value of the $500 after 2 years is

Suppose you will receive $500 at some point in the future.If the annual interest rate is 7.5 percent,then the present value of the $500 is

Suppose the interest rate is 10 percent.Which of the following payments has the largest present value?

Discounting refers directly to

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 5.5 percent.The future value of the $500 is

One way to characterize the difference between compounding and discounting is to say that

James offers you $1,000 today or $X in 7 years.If the interest rate is 4.5 percent,then you would prefer to take the $1,000 today if and only if

If the interest rate is 4 percent,then you would be equally happy if you received a gift of either $100 today or a gift of

If the interest rate is 7.5 percent,then what is the present value of $4,000 to be received in 6 years?

Imagine that someone offers you $X today or $1,500 in 5 years.If the interest rate is 4 percent,then you would prefer to take the $X today if and only if

A manufacturing company is thinking about building a new factory.The factory,if built,will yield the company $300 million in 7 years,and it would cost $220 million today to build.The company will decide to build the factory if the interest rate is

Suppose you are deciding whether or not to buy a particular bond for $5,980.17.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $10,000.You will buy the bond today if the interest rate is

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 3 percent.The future value of the $500 after 1 year is

Compounding refers directly to

In which of the following instances is the present value of the future payment the largest?

Suppose your uncle offers you $100 today or $150 in 10 years.You would prefer to take the $100 today if the interest rate is

Imagine that someone offers you $100 today or $200 in 10 years.You would prefer to take the $100 today if the interest rate is

Suppose you put $350 into a bank account today.Interest is paid annually and the annual interest rate is 6 percent.The future value of the $350 after 4 years is

Suppose you are deciding whether to buy a particular bond.If you buy the bond and hold it for 4 years,then at that time you will receive a payment of $10,000.If the interest rate is 6 percent,you will buy the bond if its price today is no greater than