Question 1

The rule of 70 applies to a growing savings account but not to a growing economy.

Accepted Answer

The rule of 70 applies to a growing economy as well as a growing savings account. It is used to estimate the number of years it takes for a particular variable (such as GDP or population) to double at a given growth rate.

Question 2

The present value of $100 to be paid in two years is less than the present value of $100 to be paid in three years.

Accepted Answer

The present value of a sum of money to be received in the future decreases as the time to receipt increases, due to the time value of money. Therefore, $100 to be paid in two years has a higher present value than $100 to be paid in three years.

Question 3

As the interest rate increases, the present value of future sums decreases, so firms will find fewer investment projects profitable.

Accepted Answer

This is because higher interest rates mean that the cost of borrowing money increases, making it more expensive for firms to finance their investments. Additionally, higher interest rates mean that the return on investments must be higher to justify the cost of borrowing. As a result, firms will be more selective in the investment projects they choose to pursue.

Question 4

People who are risk averse dislike bad outcomes more than they like comparable good outcomes.

Accepted Answer

This statement is true. Risk averse individuals prioritize avoiding negative outcomes over achieving positive outcomes, even if the potential rewards are comparable.

Question 5

Risk aversion simply means that people dislike bad things to happen.

Accepted Answer

Risk aversion refers to the preference for avoiding losses over acquiring equivalent gains; it's about the preference for certainty over uncertainty, not just disliking bad things.

Question 6

ZZL Corporation has the opportunity to undertake an investment project that will cost $20,000 today. If the interest rate is 20 percent and if the project will yield the company $30,000 in 3 years, then ZZL will undertake the project.

Accepted Answer

The answer of ZZL Corporation has the opportunity to undertake...

Question 7

Risk-averse individuals like good things more than they dislike comparable bad things.

Accepted Answer

Risk-averse individuals dislike losses more than they like comparable gains, which is a reflection of loss aversion, a concept in prospect theory.

Question 8

The sooner a payment is received and the higher the interest rate, the greater the present value of a future payment.

Accepted Answer

The present value of a future payment decreases as the interest rate increases or the payment is received later, because present value is inversely related to the interest rate and the time until payment.

Question 9

The future value of $1 saved today is $1/(1 + r).

Accepted Answer

The future value of $1 saved today is actually $1 * (1 + r)^n, where r is the interest rate and n is the number of periods. The formula $1/(1 + r) represents the present value of $1 received in the future, not its future value.

Question 10

PZX Corporation has the opportunity to undertake an investment project that will cost $10,000 today and yield the company $13,310 in 3 years. PZX will forgo the project if the interest rate is higher than 10 percent.

Accepted Answer

To calculate the interest rate that would make the project unprofitable, we can use the formula: PV = FV / (1 + r)^n, where PV is the present value (in this case, $10,000), FV is the future value (in this case, $13,310), r is the interest rate, and n is the number of years (in this case, 3).

Solving for r, we get: r = (FV / PV)^(1/n) - 1 = ($13,310 / $10,000)^(1/3) - 1 = 0.1097 or 10.97%.

Since this interest rate is higher than 10 percent, PZX will forgo the project. Therefore, the statement is true.

Question 11

If the interest rate is 8 percent, then the present value of $1,000 to be received in 4 years is $735.03.

Accepted Answer

The present value (PV) of $1,000 to be received in 4 years at an 8 percent interest rate can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value ($1,000), r is the annual interest rate (0.08), and n is the number of years (4). Plugging in these values gives PV = $1,000 / (1 + 0.08)^4 = $1,000 / 1.36049 = $735.03.

Question 12

An increase in the interest rate causes a decrease in the future value of $1,000 that you have in a bank account today.

Accepted Answer

An increase in the interest rate increases the future value of money saved in a bank account because the amount of interest earned on the saved money will be higher.

Question 13

A company that can build a project that will cost $50,000, but returns $52,000 in one year would make a good decision by turning this project down if the interest rate were 3 percent.

Accepted Answer

The company would make a profit of $2,000 ($52,000 - $50,000) in one year, which is a return of 4% ($2,000 / $50,000 x 100). This is higher than the interest rate of 3%, so it would be a good decision for the company to undertake the project.

Question 14

If a savings account pays 5 percent annual interest, then the rule of 70 tells us that the account value will double in approximately 14 years.

Accepted Answer

The rule of 70 is a quick way to estimate how long it will take for an investment to double in value, given a certain interest rate. To use the rule of 70, simply divide 70 by the interest rate (as a percentage). In this case, 70/5 = 14, so the account value will double in approximately 14 years.

Question 15

If you are faced with the choice of receiving $500 today or $800 6 years from today, you will be indifferent between the two possibilities if the interest rate is 8.148 percent.

Accepted Answer

Using the formula for the present value, $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the interest rate, and $n$ is the number of periods, we can calculate the present value of $800 received 6 years from today at an 8.148% interest rate. Plugging in the values, $PV = \frac{800}{(1 + 0.08148)^6}$, which equals approximately $500. This means at an 8.148% interest rate, you would be indifferent between receiving $500 today or $800 in 6 years, as their present values are equivalent.

Question 16

The concept of present value helps explain why the quantity of loanable funds demanded decreases when the interest rate increases.

Accepted Answer

Present value is the idea that money available in the present is worth more than the same amount of money in the future. This means that as the interest rate increases, the present value of future loan repayments decreases, causing a decrease in demand for loanable funds. This is because borrowers are less inclined to borrow money at higher interest rates since they will have to pay more back in the future, resulting in a decrease in the quantity of loanable funds demanded.

Question 17

The market for insurance is an example of diversification.

Accepted Answer

The market for insurance involves different types of insurance (e.g. auto, health, life, property) and serves diverse customer needs, making it an example of diversification.

Question 18

According to the rule of 70, if you earn an interest rate of 3.5 percent, your savings will double about every 20 years.

Accepted Answer

The answer of According to the rule of 70, if...

Question 19

The present value of any future sum of money is the amount that would be needed today, at current interest rates, to produce that future sum.

Accepted Answer

This statement is true. Present value is a fundamental concept in finance and is used to determine the value of future cash flows in today's dollars. The calculation takes into account the time value of money and the current interest rate to determine the amount that would need to be invested today to achieve a desired future sum.

Question 20

The present value of a payment of $500 to be made two years from today is greater if the interest rate is 7% than if it is 6%.

Accepted Answer

The present value of a future payment decreases as the interest rate increases, because a higher rate means a greater discount is applied to the future payment.

Quiz 27: Tools of Finance