Question 1

Roger has the opportunity to invest $100,000 in two different assets. The investment in Asset #1 will have a present value of $120,000. The investment in Asset #2 is expected to have a future value of
$140,000 in four years. If the market interest rate is 5 percent a year, which one would be the better
Investment?

Accepted Answer

To compare the two investments, we need to find the present value of Asset #2. Using the formula for present value of a single amount: 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 periods.

PV = $140,000 / (1 + 0.05)^4 = $113,350.60

Therefore, the present value of Asset #2 is $113,350.60, which is less than the present value of Asset #1 ($120,000). Therefore, Asset #1 is the better investment.

Question 2

Other factors constant, the present value will be larger,

Accepted Answer

The present value of a future amount of money is inversely related to the time period until receipt; the shorter the time period, the larger the present value, because there is less time for the discounting effect of the interest rate to apply.

Question 3

A bank account pays 4 percent interest per year. If you deposit $1,000 into this account at the start of each year for three years, how much will your account balance be at the end of three years?

Accepted Answer

In the first year, the account balance will be $1000. 
In the second year, the account balance will be $1000 (initial deposit) + $40 (interest on the first year's balance) + $1000 (second year's deposit)= $2040. 
In the third year, the account balance will be $2040 (second year's balance) + $81.6 (interest on the second year's balance) + $1000 (third year's deposit) = $3121.60.

Rounded to the nearest dollar, the account balance at the end of three years will be $3,246, which is choice B.

Question 4

Matt, a star basketball player, is looking to join a new NBA team. The Bulls are offering him $24 million for one year. The Heat is offering him $10 million this year and $7.0 million in each of the next
Two years. The market interest rate is 5 percent. What is the present value of the offer from The
Heat in millions (rounded to the nearest one hundred thousand dollars)?

Accepted Answer

To compare the two offers, we need to calculate the present value of the Heat's offer. Using a financial calculator, the present value of the Heat's offer is:

PV = -$10,000,000 + ($7,000,000 / 1.05) + ($7,000,000 / 1.05^2) 
PV = $20,850,318

Therefore, the present value of the Heat's offer is $20.85 million, which is less than the Bulls' offer of $24 million. Therefore, the best choice is to choose the Bulls' offer. However, if Matt values the flexibility of receiving the money over three years instead of one, he may still choose the Heat's offer.

Question 5

You estimate that a piece of real estate for investment will be worth $700,000 in ﬁve years. The current interest rate is 3 percent. What is the present value of this investment?

Accepted Answer

The present value (PV) can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value ($700,000), r is the interest rate (3% or 0.03), and n is the number of periods (5 years). Plugging in the values, PV = $700,000 / (1 + 0.03)^5 ≈ $604,000.

Question 6

A promised amount $FV n years into the future is worth how much today, if the interest rate is i percent per year?

Accepted Answer

This is the formula for present value of a future payment, taking into account the time (n) and the interest rate (i).

Question 7

Orange Computers, Inc., is planning to spend $200,000 on the promotion of its new portable music player next year. The current market interest rate is 5 percent. What is the present value of this
Promotional budget?

Accepted Answer

The present value (PV) of the promotional budget can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value ($200,000), r is the interest rate (5% or 0.05), and n is the number of periods (1 year). Plugging in the values, we get PV = $200,000 / (1 + 0.05)^1 = $200,000 / 1.05 = $190,476.

Question 8

The present value model of investment states that an asset's current price should be equal to the

Accepted Answer

The present value model of investment states that an asset's current price should be equal to the sum of the present values of all of its future payments or earnings. This takes into account the time value of money, meaning that money in the future is worth less than money in the present. Therefore, the model values future payments or earnings less than current ones by discounting them. The sum of these discounted future cash flows should equal the asset's current price.

Question 9

Kick is looking to play for a U.S. MLS team. D.C. United is offering him $50 million for his ﬁrst year. The Chicago Fire is offering him $25 million his ﬁrst year and $10 million per year for the following
Three years. The market interest rate is 5 percent. Which offer is the better deal in terms of present
Value in millions?

Accepted Answer

The present value of the Chicago Fire offer is $52.2 million, which is higher than the present value of the D.C. United offer of $50 million.

Question 10

Xavier is a baseball player negotiating a contract to play for a team for one year. He is usually paid $10 million a year for playing, but the salary cap for his team means that he will have to be paid $5
Million this year and the remainder next year. If the interest rate is 8 percent, how much should that
Remaining amount be next year?

Accepted Answer

The present value of the remaining amount next year is $5 million. The future value of this amount at 8% interest for one year is $5.4 million.

Question 11

Other factors constant, the future value will be smaller,

Accepted Answer

The future value of an investment is directly related to the time period; the shorter the time period, the smaller the future value, assuming other factors remain constant.

Question 12

You would like to have $50,000 for a new car in six years. If you deposit money today in a bank CD that pays 4 percent per year, how much must your deposit be?

Accepted Answer

Using the formula for compound interest, we have:

Future value = Present value x (1 + interest rate)^time

Plugging in the given information, we get:

$50,000 = Present value x (1 + 0.04)^6

Solving for Present value, we get:

Present value = $39,516 (rounded to the nearest dollar)

Therefore, the best choice is B.

Question 13

A bond that pays annual interest (or coupons) and a face value at maturity will fetch a price today that is equal to the

Accepted Answer

A bond that pays annual interest (or coupons) and a face value at maturity can be valued using the present value of its future cash flows. This means that we need to discount each of the future cash flows (annual coupon payments and face value) back to their present value using the appropriate discount rate. So, the price of the bond today will be the sum of the present values of all the future cash flows. Therefore, the correct choice is C, which says the price of the bond today is equal to the present value of its annual coupons and face value.

Question 14

You deposit $5,000 in a 5-year bank CD that pays 3 percent interest per year. How much will you get from this deposit at maturity?

Accepted Answer

The formula for calculating the maturity amount of a CD is:
M = P(1 + r/n)^(nt)
Where,
M = maturity amount
P = principal amount, i.e., $5,000
r = interest rate in decimal form, i.e., 0.03
n = number of times interest is compounded per year, i.e., 1
t = number of years, i.e., 5

Plugging in the values, we get:
M = 5000(1 + 0.03/1)^(1*5)
M = 5796.05

Rounding to the nearest dollar, the answer is $5,796. Therefore, the best choice is C.

Question 15

The correct formula that relates present value (PV) to future value (FV), if interest rate is i percent per year over n years is

Accepted Answer

The correct formula that relates present value (PV) to future value (FV), if interest rate is i percent per year over n years is PV = FV / (1+i)^n. This formula takes into account the time value of money and allows for the calculation of the present value of a future sum of money, considering the effects of interest. Choice A is the formula for calculating future value with compound interest. Choice B is the formula for calculating future value with simple interest. Choice D is an incorrect formula that does not take into account the exponent on (1+i) needed to properly compound interest over a number of years.

Question 16

A bond that pays no annual interest (or coupons) and has a face value at maturity will fetch a price today that is equal to the

Accepted Answer

Since the bond pays no annual interest or coupons, the only cash flow that the investor will receive is the face value at maturity. Therefore, the price today will be the present value of that face value, which is given by choice D.

Question 17

Tracy won a $100 million jackpot. She can receive the jackpot as a $5 million payment each year for 20 years, or she can ask to receive the present value of all those payments all at once now. Assume
An annual interest rate of 5 percent. If she decides to take the present value payment, about how
Much will she receive?

Accepted Answer

The present value of an annuity can be calculated using the formula PV = Pmt × [(1 - (1 + r)^-n) / r], where Pmt is the annual payment, r is the interest rate, and n is the number of periods. Plugging in the values: PV = $5 million × [(1 - (1 + 0.05)^-20) / 0.05] ≈ $62.3 million.

Question 18

A bond pays a coupon (or interest) rate of 5 percent each year for ﬁve years, with a future (face) value of $200. If the bond were sold today, what would be the present value of the bond?

Accepted Answer

To find the present value of the bond, we need to discount the future value of $200 back to present. The formula to do this is:

Present value = Future value / (1 + r)^n

where r is the discount rate (or interest rate) and n is the number of periods. In this case, n = 5 (since the bond is held for 5 years) and r is not given explicitly.

However, we know that the bond pays a coupon rate of 5 percent each year, which means that the discount rate is also 5 percent. So we can plug in r = 0.05 and n = 5 to get:

Present value = $200 / (1 + 0.05)^5 
= $157.10 (rounded to the nearest penny)

Therefore, the best choice is B.

Question 19

A manufacturing ﬁrm takes out a $500,000 loan to expand its plant. The loan has an annual interest rate of 7 percent. What would be the total compounded interest on the loan at the end of ﬁve years,
Excluding the principal?

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt) - P, where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $500,000, r = 7% or 0.07, n = 1 (annual compounding), and t = 5. Plugging these values into the formula, we get:

A = $500,000(1 + 0.07/1)^(1*5) - $500,000
A = $201,275

Therefore, the total compounded interest on the loan at the end of five years, excluding the principal, is $201,275 - $500,000 = -$298,725 (or a loss of $298,725). However, since the question asks for the total compounded interest only (and not the final amount), the answer is D) $201,275.

Question 20

Joe and Linda have the opportunity to purchase a new home. The house in Glen Oaks is currently worth $250,000 but is predicted to be worth $270,000 in a year. What is the rate of appreciation for
The house from one year to the next?

Accepted Answer

The answer of Joe and Linda have the opportunity to...

Quiz 17: Financial Economics