Question 1

You won the "$1,000 per year forever" lottery. You decided to convert such prize into a lump sum payment. The interest rate is 2% per year. How much is this lump sum payment ?

Accepted Answer

To convert a perpetual cash flow into a lump sum payment, we need to use the perpetuity formula:
PV = CF/i
where PV is the present value, CF is the cash flow, and i is the interest rate.
In this case, the cash flow is $1,000 per year forever, so CF = $1,000.
The interest rate is 2% per year, so i = 0.02.
Plugging in these values, we get:
PV = $1,000/0.02 = $50,000
Therefore, the lump sum payment is $50,000. Option C is the correct choice.

Question 2

A major corporation hires high school students on a part-time basis. It offers a reward of $5,000 to any of its high school seniors who graduate college in four years. What is the present value of that reward to a student who just finished her junior year of high school, assuming a nominal rate of interest of 8%?

Accepted Answer

The answer of A major corporation hires high school students...

Question 3

You sign a contract to pay $1000 next year for the refrigerator you bought today. The rate of inflation is 10% and the real interest rate is 7%. Alternatively, you could pay $875 today. What should you do to save the most money?

Accepted Answer

The answer of You sign a contract to pay $1000...

Question 4

Individuals who lease a new car

Accepted Answer

Individuals who lease a new car typically have a higher discount rate than those who buy. This is because leasing often involves preferring to pay a smaller amount upfront and more over time, indicating a preference for current consumption over future savings, which is characteristic of a higher discount rate.

Question 5

Suppose there is no inflation, and the current interest rate is 4% per year. Erin plans to open a savings account and deposit $100 annually for the next 5 years. She plans to leave this money untouched for 10 more years. At the end of the period, the balance of her savings account will be

Accepted Answer

To calculate the balance of the savings account after 15 years, we can break down the problem into two parts:
1. Finding the balance of the savings account after the first 5 years (let's call this amount X).
2. Finding the balance of the savings account after the next 10 years, starting with X.

Part 1: Finding X
Erin plans to deposit $100 annually for the next 5 years. Therefore, at the end of the fifth year, the balance of her savings account will be:
X = 100(1.04)^4 + 100(1.04)^3 + 100(1.04)^2 + 100(1.04)^1 + 100(1.04)^0
X = 100(1.04^4 + 1.04^3 + 1.04^2 + 1.04 + 1)

Using a calculator, we get X = $557.03

Part 2: Finding the final balance after 10 more years, starting with X
Since Erin plans to leave the money untouched for 10 more years, we can simply compound the interest on X for 10 more years. This gives us:
Final balance = X(1.04)^10

Substituting X = $557.03 into the equation, we get:

Final balance = $557.03(1.04)^10
Final balance = $907.38

Therefore, the correct answer is D, which is equal to $2500(1.04^5 - 1)(1.04)^10. This is the same as $2500(1.04^15 - 1).

Question 6

Suppose $100 is deposited in a bank account paying 5% compounded annually. If the interest earned is X after 5 years, then the interest earned will be 2X after 10 years.

Accepted Answer

Because of compounding, the balance on which interest is earned grows over time. Thus, the interest earned in years 6 to 10 will exceed the interest earned in years 1 to 5.

Question 7

A firm has to decide between two projects that cost $10,000 each. Project A will provide a revenue $10,700 one year from now, while Project B will provide a revenue of $12,200 two years from now. The interest rate is 10% per year. This firm

Accepted Answer

The answer of A firm has to decide between two...

Question 8

A firm should make an investment if the expected return is greater than

Accepted Answer

The expected return should be greater than the opportunity cost of the investment. Opportunity cost is the return that could have been earned from the next best alternative use of the funds. If the expected return is less than the opportunity cost, the firm would be better off investing in the next best alternative. Therefore, the investment should only be made if the expected return is greater than the opportunity cost.

Question 9

If an asset has a present value of $50 and appreciates at an interest rate of 4%, what is the asset's future value in 47 compounding periods?

Accepted Answer

Using the formula for future value with compounding:

FV = PV x (1 + r)^n

Where:
PV = Present Value
r = Interest Rate
n = Number of compounding periods

Plugging in the given values:

FV = $50 x (1 + 0.04)^47
FV = $50 x 2.718117^47
FV ≈ $316.56

Therefore, the closest answer choice is B, Approximately $316.

Question 10

Suppose there is no inflation, and the current interest rate is 5% per year. Sarah plans to open a savings account and deposit $100 annually for the next 14 years. At the end of the period, the balance of her savings account will be

Accepted Answer

The formula to calculate the future value of an annuity is: FV = P * ((1 + r)^n - 1) / r where P is the annual payment, r is the interest rate, and n is the number of years. Substituting the given values, we get: FV = 100 * ((1 + 0.05)^14 - 1) / 0.05 FV = $2,464.10 Therefore, the balance of Sarah's savings account at the end of the 14-year period will be $2,464.10. Option B, 2000(1.05¹⁴ - 1), is the closest choice to this value. The other options either do not have the correct formula or have incorrect calculations.

Question 11

The Net Present Value approach to investment results in an investment being undertaken only if

Accepted Answer

The Net Present Value (NPV) approach to investment involves calculating the present value of all cash inflows and outflows associated with a particular investment, and subtracting the cash outflows from the cash inflows to arrive at the net present value. If the net present value is positive, then the investment is expected to generate a return that exceeds the cost of capital and is therefore considered worthwhile. If the net present value is zero or negative, the investment would not be undertaken as it would generate a return less than the cost of capital. Therefore, choice A is the correct answer.

Question 12

Suppose a new cost-saving device will generate $1,000 net savings per year to a firm. The device costs $10,000. Should the firm purchase the device?

Accepted Answer

To determine whether the firm should purchase the device, information about the firm's cost of capital, the device's useful life, and other potential investments is needed. Without this, we cannot assess the return on investment or compare it to alternatives.

Question 13

As the interest rate increases, the present value of a future payment

Accepted Answer

The present value of a future payment decreases as the interest rate increases, because the higher interest rate makes the future payment worth less today.

Question 14

Jerry wishes to retire in 5 years with $1 million in his bank account. If the account pays 4% and his current balance is $500,000, how much must he deposit at the beginning of each of the next five years for his wish to come true? The amount must be the same each year.

Accepted Answer

The answer of Jerry wishes to retire in 5 years...

Question 15

A state lottery has a Million Dollar Lottery game that pays $1,000 a week for life. Assuming a 6% nominal rate of interest and generously assuming an infinite lifetime, can this game be called a "Million Dollar Lottery"?

Accepted Answer

The answer of A state lottery has a Million Dollar...

Question 16

A firm has to choose between projects X and Y. Project X's internal rate of return is positive. If the cash flow of project Y is discounted at project X's internal rate of return, this firm will

Accepted Answer

If the cash flow of project Y, when discounted at project X's internal rate of return (IRR), results in a negative net present value (NPV), it means project Y is less desirable than project X at that rate. Therefore, the firm will choose project X.

Question 17

If an asset has a future value of $120, a present value of $30, and an interest rate of 4%, how many periods of compounding are there?

Accepted Answer

The answer of If an asset has a future value...

Question 18

If the interest rate is positive, the future value of an interest bearing investment is always larger than the present value.

Accepted Answer

FV = PV ∗ (1 + i)^t. If the interest rate is positive, the future value will always be greater than the present value.

Question 19

Interest rates are positive because inflation makes purchases more expensive in the future than today.

Accepted Answer

Even if inflation were zero, interest rates would be positive since people prefer present consumption to future consumption.

Question 20

In an economy with no inflation, explain why interest rates are positive.

Accepted Answer

The answer of In an economy with no inflation, explain...

Quiz 16: Interest Rates, Investments, and Capital Markets