Question 1

Consider a two-year investment: Given a constant and positive interest rate, the interest earned in the second year will be greater than the interest earned in the first year (assuming annual compounding).

Accepted Answer

This is because the interest earned in the second year will not only be based on the initial principal, but also on the interest earned in the first year. Therefore, the interest will compound and accumulate, resulting in a greater amount earned in the second year.

Question 2

An investment promises a payoff of $195 two and one-half years from today. At a discount rate of 7.5% per year, what is the present value of this investment?
A) $162.03
B) $162.75
C) $169.47
D) There is not enough information to answer this question.

Accepted Answer

We can use the formula for present value of a future sum, which is: 
PV = FV / (1 + r)^n 
where PV is the present value, FV is the future value, r is the discount rate, and n is the number of years.
Substituting the given values, we get: 
PV = $195 / (1 + 0.075)^2.5 
PV = $162.75 (rounded to the nearest cent) 
Therefore, the answer is choice B.

Question 3

Which of the following actions will INCREASE the present value of an investment?
A) Decrease the interest rate.
B) Decrease the future value.
C) Increase the amount of time.
D) All of the above will increase the present value.

Accepted Answer

Decreasing the interest rate increases the present value of an investment because the present value is inversely related to the interest rate. Lower interest rates result in higher present values.

Question 4

Your parents plan to spend $20,000 on a car for you upon graduation from college. If you will graduate in three years and your parents can earn 4.125% annually on their investment, how much money must they set aside today for your car?
A) $20,000
B) $17,704
C) $17,716
D) $16,387

Accepted Answer

Using the present value formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods, we can solve for the present value that needs to be set aside:
PV = 20,000 / (1 + 0.04125)^3
PV = 20,000 / 1.13073315625
PV = $17,715.80
So, the correct answer is C) $17,716, which is the closest option to the calculated present value.

Question 5

The TVM equation  can be algebraically manipulated to solve for any of the variables EXCEPT for the time period n.

Accepted Answer

The TVM equation can be rearranged to solve for any of the variables, including the time period n.

Question 6

Sam wishes to invest $8,000 into an account earning 6% compounded annually. If he invests the money today, how much will be in the account in 6 years? If he waits three years before investing his $8,000 and invests that money for three years, will he earn one-half of the interest earned in the first scenario since he had the same amount invested at the same rate but for only one-half of the time? Explain how you arrived at your answer.

Accepted Answer

The answer of Sam wishes to invest $8,000 into an...

Question 7

Consider the TVM equation: A decrease in the interest rate will decrease the future value, other things remaining equal.

Accepted Answer

This statement is true. The future value of an investment decreases as the interest rate decreases because there is less return on the investment.

Question 8

$5,000 invested at an annual rate of 6% for 3 years has a smaller future value than $5,000 invested at an annual rate of 3% for 6 years.

Accepted Answer

This is because the longer period of time at a lower interest rate allows for more compounding, resulting in a larger future value.

Question 9

Consider the TVM equation: The future value is always greater than the present value, even if the interest rate is negative.

Accepted Answer

The future value can be less than the present value if the interest rate is negative, as negative interest rates would decrease the value of the investment over time.

Question 10

In five years your oldest child will be in 8^th grade, at which point you and your family plan to vacation in Europe. You estimate that you will need $20,000 for the trip. How much do you need to set aside today if you can place your money in an investment vehicle earning an average of 4.50% per year? A) $14,961 B) $15,073 C) $16,049 D) $16,058

Accepted Answer

To calculate the amount needed today, we can use the present value formula:

Present Value = Future Value / (1 + r)n

Where:
r = interest rate
n = number of years until the future value is needed

Plugging the given values into the formula, we get:

Present Value = $20,000 / (1 + 0.045)5

Present Value = $16,048.84

Rounding off to the nearest dollar gives the answer as $16,049, which is option C.

Question 11

$100 invested at a rate of 5% for 10 years has the same future value as $100 invested at 10% compounded annually for 5 years.

Accepted Answer

The future value of an investment is calculated using the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. For the first scenario (5% for 10 years), the future value is $100(1 + 0.05)^10 = $162.89. For the second scenario (10% for 5 years), the future value is $100(1 + 0.10)^5 = $161.05. Therefore, the future values are not the same.

Question 12

Your university is running a special offer on tuition. This year's tuition cost is $18,000. Next year's tuition cost is scheduled to be $19,080. The university offers to discount next year's tuition at a rate of 6% if you agree to pay both years' tuition in full today. How much is the total tuition bill today if you take the offer?
A) $18,000
B) $34,981
C) $37,080
D) $36,000

Accepted Answer

The answer of Your university is running a special offer...

Question 13

Consider the TVM equation: A decrease in the time period will increase the future value, other things remaining equal.

Accepted Answer

The TVM equation states that a decrease in the time period will decrease the future value, other things remaining equal.

Question 14

Consider the TVM equation: An increase in the present value will decrease the future value, other things remaining equal.

Accepted Answer

The TVM (Time Value of Money) equation suggests that the future value increases with an increase in the present value, assuming the interest rate and time period remain constant.

Question 15

You have purchased a Treasury bond that will pay $10,000 to your newborn child in 15 years. If this bond is discounted at a rate of 3.875% per year, what is today's price (present value) for this bond?
A) $8,417
B) $8,500
C) $5,654
D) $10,000

Accepted Answer

The answer of You have purchased a Treasury bond that...

Question 16

Which of the following formulas is correct for finding the present value of an investment? A) FV= B) PV=FV × (1+r)ⁿ C) PV=FVⁿ × (1+r) D) PV=FV ×

Accepted Answer

The answer of Which of the following formulas is correct...

Question 17

You intend to buy a vacation home in seven years and plan to have saved $50,000 for a down payment. How much money would you have to place today into an investment that earns 8% per year to have enough for your desired down payment?
A) $29,175
B) $29,100
C) $37,065
D) $25,000

Accepted Answer

The answer of You intend to buy a vacation home...

Question 18

A furniture store has a sofa on sale for $399.00, with the payment due one year from today. The store is willing to discount the price at an annual rate of 5% if you pay today. What is the amount if you pay today?
A) $380.
B) $399
C) $419
D) $394

Accepted Answer

The answer of A furniture store has a sofa on...

Question 19

Which of the following actions will DECREASE the present value of an investment?
A) Decrease the interest rate.
B) Decrease the future value.
C) Decrease the amount of time.
D) All of the above will decrease the present value.

Accepted Answer

The answer of Which of the following actions will DECREASE...

Question 20

If your bank offers a 5% annual rate of return compounded annually, then at the end of one year your $1.00 deposit would grow by $0.05 to $1.05. However, in the second year, your deposit would increase by $0.0525 to a total ending value of $1.1025. Explain why the second year earns more interest on the investment than the first year.

Accepted Answer

The answer of If your bank offers a 5% annual...

Quiz 3: The Time Value of Money Part 1

Consider a two-year investment: Given a constant and positive interest rate, the interest earned in the second year will be greater than the interest earned in the first year (assuming annual compounding).

An investment promises a payoff of $195 two and one-half years from today. At a discount rate of 7.5% per year, what is the present value of this investment?

Which of the following actions will INCREASE the present value of an investment?

Your parents plan to spend $20,000 on a car for you upon graduation from college. If you will graduate in three years and your parents can earn 4.125% annually on their investment, how much money must they set aside today for your car?

The TVM equation can be algebraically manipulated to solve for any of the variables EXCEPT for the time period n.

Consider the TVM equation: A decrease in the interest rate will decrease the future value, other things remaining equal.

$5,000 invested at an annual rate of 6% for 3 years has a smaller future value than $5,000 invested at an annual rate of 3% for 6 years.

Consider the TVM equation: The future value is always greater than the present value, even if the interest rate is negative.

$100 invested at a rate of 5% for 10 years has the same future value as $100 invested at 10% compounded annually for 5 years.

Consider the TVM equation: A decrease in the time period will increase the future value, other things remaining equal.

Consider the TVM equation: An increase in the present value will decrease the future value, other things remaining equal.

You have purchased a Treasury bond that will pay $10,000 to your newborn child in 15 years. If this bond is discounted at a rate of 3.875% per year, what is today's price (present value) for this bond?

Which of the following formulas is correct for finding the present value of an investment?

You intend to buy a vacation home in seven years and plan to have saved $50,000 for a down payment. How much money would you have to place today into an investment that earns 8% per year to have enough for your desired down payment?

A furniture store has a sofa on sale for $399.00, with the payment due one year from today. The store is willing to discount the price at an annual rate of 5% if you pay today. What is the amount if you pay today?

Which of the following actions will DECREASE the present value of an investment?