Question 1

Other things the same, an increase in the interest rate makes the quantity of loanable funds demanded

Accepted Answer

An increase in the interest rate makes borrowing more expensive, which decreases the quantity of loanable funds demanded and reduces investment spending, as firms are less likely to borrow money for investment projects when interest rates are high.

Question 2

A firm has three different investment options. Option A will give the firm $10 million at the end of one year, $10 million at the end of two years, and $10 million at the end of three years. Option B will give the firm $15 million at the end of one year, $10 million at the end of two years, and $5 million at the end of three years. Option C will give the firm $30 million at the end of one year, and nothing thereafter. Which of these options has the highest present value?

Accepted Answer

The answer of A firm has three different investment options....

Question 3

Sari puts $100 into an account with an interest rate of 10 percent. According to the rule of 70, about how much does she have at the end of 21 years?

Accepted Answer

The rule of 70 is a way to estimate the number of years it takes for an investment to double in value at a given annual rate of return by dividing 70 by the interest rate. With a 10 percent interest rate, it takes about 7 years for the investment to double (70/10 = 7). In 21 years, the investment doubles 3 times (21/7 = 3). Starting with $100, after the first 7 years it doubles to $200, after 14 years it doubles again to $400, and after 21 years it doubles once more to $800.

Question 4

Figure 27-1
The following figure shows a utility function for Ren. 
-Refer to Figure 27-1. From the appearance of the utility function, we know that

Accepted Answer

The utility function likely shows diminishing marginal utility, indicating that Ren gains less additional satisfaction from each additional dollar, which is characteristic of risk aversion.

Question 5

A University of Iowa basketball standout is offered a choice of contracts by the New York Liberty. The first one gives her $100,000 one year from today and $100,000 two years from today. The second one gives her $132,000 one year from today and $66,000 two years from today. As her agent, you must compute the present value of each contract. Which of the following interest rates is the lowest one at which the present value of the second contract exceeds that of the first?

Accepted Answer

The present value of the first contract is $100,000/(1+r) + $100,000/(1+r)^2. The present value of the second contract is $132,000/(1+r) + $66,000/(1+r)^2. The second contract will have a higher present value if $132,000/(1+r) + $66,000/(1+r)^2 > $100,000/(1+r) + $100,000/(1+r)^2. This inequality simplifies to $32,000/(1+r)^2 > 0, which is true for all positive values of r. Therefore, the lowest interest rate at which the present value of the second contract exceeds that of the first is 0%.

Question 6

Suppose you win a small lottery and you are given the following choice: You can receive (1) an immediate payment of $5,000 or (2) two annual payments, each in the amount of $2,700, with the first payment coming one year from now, and the second payment coming two years from now. You would choose to take the two annual payments if the interest rate is

Accepted Answer

The answer of Suppose you win a small lottery and...

Question 7

Happy Trails, a bicycle rental company, is considering purchasing three additional bicycles. Each bicycle would cost them $249.66. At the end of the first year the increase to their revenues would be $140 per bicycle. At the end of the second year the increase to their revenues again would be $140 per bicycle. Thereafter, there are no increases to their revenues. At which of the following interest rates is the sum of the present values of the additional revenues closest to the price of a bicycle?

Accepted Answer

The answer of Happy Trails, a bicycle rental company, is...

Question 8

Mixster Concrete Company is considering buying a new cement truck. The owners and their accountants decide that this is the profitable thing to do. Before they can buy the truck, the interest rate and price of trucks change. In which case do these changes both make them less likely to buy the truck?

Accepted Answer

When interest rates rise, the cost of borrowing money to buy the truck increases, making it less affordable. Similarly, when truck prices rise, the initial investment required also increases. Both these factors together make it less likely for Mixster Concrete Company to proceed with the purchase.

Question 9

Figure 27-1
The following figure shows a utility function for Ren. 
-Refer to Figure 27-1. Suppose the vertical distance between the points (0, A) and (0, B) is 9. If his wealth increased from $1,050 to $1,350, then

Accepted Answer

The vertical distance between points on a utility curve represents the change in utility or subjective well-being. Since utility functions typically exhibit diminishing marginal utility of wealth, an increase in wealth leads to a smaller increase in utility as wealth grows. Therefore, even though Ren's wealth increases, the subjective measure of his well-being would increase by less than the vertical distance between any two points on the curve, assuming the curve represents a typical utility function with diminishing marginal utility.

Question 10

In answering which of the following questions would you find it necessary to calculate a present value?

Accepted Answer

Calculating present value is necessary to determine if the future cash inflow of $5 million is worth the $4 million investment today.

Question 11

Figure 27-1
The following figure shows a utility function for Ren. 
-Refer to Figure 27-1. From the appearance of the utility function, we know that

Accepted Answer

The utility function's appearance, which typically reflects a person's preferences under uncertainty, suggests that Ren is risk-averse. A risk-averse individual prefers investments with less risk for the same level of expected return, hence preferring a portfolio with a lower standard deviation (1 percent) over one with a higher standard deviation (5 percent), assuming the average return is the same (6 percent).

Question 12

Xavier puts $7,000 into each of two different assets. The first asset pays 14 percent interest and the second pays 7 percent. According to the rule of 70, what is the approximate difference in the value of the two assets after 10 years?

Accepted Answer

The answer of Xavier puts $7,000 into each of two...

Question 13

For a risk averse person,

Accepted Answer

Risk-averse individuals experience more discomfort from losing a certain amount of money than the pleasure they gain from winning the same amount. This is because their utility function typically exhibits diminishing marginal utility of wealth, meaning that as wealth increases, the additional satisfaction (utility) gained from an extra dollar decreases.

Question 14

According to the rule of 70, if the interest rate is 10 percent, about how long will it take for the value of a savings account to double?

Accepted Answer

The rule of 70 is a way to estimate the number of years it will take for an investment to double at a given annual rate of return by dividing 70 by the interest rate. So, 70 divided by 10 equals 7 years.

Question 15

Benjamin would like to double the money in his retirement account in seven years. According to the rule of 70, what rate of interest would he need to earn to attain his objective?

Accepted Answer

The rule of 70 states that to find the number of years required to double an investment at a given annual rate of return, you divide 70 by the annual rate of return. Conversely, to find the rate needed to double in a certain number of years, you divide 70 by the number of years. So, 70 divided by 7 years equals 10 percent.

Question 16

Figure 27-1
The following figure shows a utility function for Ren. 
-Refer to Figure 27-1. Suppose Ren begins with $1,050 in wealth. Starting from there,

Accepted Answer

This is based on the concept of diminishing marginal utility of wealth, which suggests that the utility gained from an additional dollar of wealth decreases as the amount of wealth increases. Therefore, the pain (or negative utility) from losing a certain amount of wealth is greater than the pleasure (or positive utility) gained from adding the same amount of wealth. This is because the utility function of wealth is typically concave, reflecting risk aversion.

Question 17

On the Internet you find the following offers for opening an online account. Which of them is the best offer if you have $2,000 to save for two years?

Accepted Answer

Option A provides the highest return despite the initial processing fee. With a 5% interest rate on $2,000 for two years, the interest earned would be $200 ($2,000 * 5% * 2), minus the $15 fee, resulting in a net gain of $185. The other options offer lower interest rates and, even with bonuses, result in lower overall returns.

Question 18

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?

Accepted Answer

The correct way to find the present value of this bond is to discount each future payment by the interest rate (r) for the period until it is received. This is represented by the formula $500/(1 + r) for the payment in one year and $10,500/(1 + r)^2 for the payment in two years, which matches option B.

Question 19

You are tearing down a building and find $1 in change that someone lost when working on the building 140 years ago. If, instead of being careless with the $1 in change, this person had deposited it into a bank and earned 2 percent interest every year for 140 years, how much would be in the account today according to the rule of 70?

Accepted Answer

The rule of 70 estimates the doubling time of an investment by dividing 70 by the interest rate. At 2% interest, the money doubles approximately every 35 years (70/2). In 140 years, the money would double 4 times (140/35), resulting in $16.

Question 20

Table 27-1
​
 $\text { Kevin's Utility Function }$
$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { W ealth } \
\text { (Dollars) }
\end{array} & \text { Utility } \
\hline 50,000 & 3,000 \
\hline 51,000 & 3,140 \
\hline 52,000 & 3,266 \
\hline 53,000 & 3,373 \
\hline
\end{array}$ ​
​
-Refer to Table 27-1. If Kevin's current wealth is $51,000, then

Accepted Answer

The utility from gaining $1,000 when Kevin's wealth is $51,000 is the difference between the utility at $52,000 and $51,000, which is 3,266 - 3,140 = 126. The utility loss from losing $1,000 when Kevin's wealth is $51,000 is the difference between the utility at $51,000 and $50,000, which is 3,140 - 3,000 = 140. Since the loss in utility (140) is greater than the gain in utility (126), and this behavior is indicative of risk aversion, option C is correct.

Quiz 27: Tools of Finance