Question 1

Which of the following is greater (answers rounded to the nearest cent)?

Accepted Answer

The answer of Which of the following is greater (answers...

Question 2

Autorola plans to invest $5,000 per year in equal annual end-of-the-year amounts at an interest rate of 6% compounded annually. How much will the firm have at the end of four years?

Accepted Answer

The answer of Autorola plans to invest $5,000 per year...

Question 3

You estimate that the little drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $150,000 per year for the next ten years. If you discount these cash flows at an annual rate of 14%, what is the present value of your expected cash flows?

Accepted Answer

The present value of an ordinary annuity can be calculated using the formula PV = C * [(1 - (1 + r)^-n) / r], where C is the cash flow per period, r is the discount rate, and n is the number of periods. Plugging in the values: PV = $150,000 * [(1 - (1 + 0.14)^-10) / 0.14] = $782,417.35.

Question 4

A trend among universities is to guarantee tuition to incoming freshmen for a four-year period. Further, the annual amount due is collected in equal payments collected every three months. Although the payments are equal as well as equally spaced, this is NOT an example of an annuity because the payments are made every three months rather than on a monthly or annual basis.

Accepted Answer

The statement is incorrect. This is still an example of an annuity, specifically a quarterly annuity.

Question 5

Which of the following choices will result in a greater future value at age 65? Choice number 1 is to invest $3,000 per year from ages 20 through 26 (a total of seven investments) into an account and then leave it untouched until you are 65 (another 39 years). Choice number 2 is to begin at age 27 and make $3,000 deposits into an investment account every year until you are 65 years old (a total of 39 investments). Each account earns an average of 10% per year. (The investments are end-of-year payments.)

Accepted Answer

The answer of Which of the following choices will result...

Question 6

Even with an interest rate of 0.0%, the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

Accepted Answer

The future value of an annuity considers the compound interest earned on the payments over time. With a 0.0% interest rate, there's no compound interest, so the future value simply equals the sum of the payments made, which does not exceed the present value of those same payments when considering time value of money principles.

Question 7

Which is greater, the present value of a five-year ordinary annuity of $300 discounted at 10%, or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

Accepted Answer

The present value of the second annuity can be calculated using the formula: PV = $300/ (1+0%) + $300/(1+10%)^2 + $300/(1+10%)^3 + $300/(1+10%)^4 + $300/(1+10%)^5 = $1,413.87. 
The present value of the first annuity can be calculated using the formula: PV = $300/(1+10%) + $300/(1+10%)^2 + $300/(1+10%)^3 + $300/(1+10%)^4 + $300/(1+10%)^5 = $1,153.09. 
Therefore, the second annuity has a greater present value because the discount rate is lower, even though the first cash flow is delayed by a year.

Question 8

The formula for the Future Value Interest Factor of an Annuity (FVIFA) is  .

Accepted Answer

The formula for the Future Value Interest Factor of an Annuity (FVIFA) is indeed 11ea6dfa_8f13_eab2_8816_3331a97d0779_TB2644_00.

Question 9

What is the future value in year twelve of an ordinary annuity cash flow of $6,000 per year at an interest rate of 4.00% per year?

Accepted Answer

The answer of What is the future value in year...

Question 10

Which is greater, the present value of a $1,000 five-year ordinary annuity discounted at 10%, or the present value of a $1,000 five-year annuity due discounted at 10%?

Accepted Answer

An annuity due is worth more than an ordinary annuity because each payment is received one period sooner. Therefore, the annuity due has a higher present value. In this case, the present value of the annuity due is $4,169.87, which is greater than the present value of the ordinary annuity at $3,790.79.

Question 11

You have the opportunity to purchase mineral rights to a property in North Dakota with expected annual cash flows of $10,000 per year for eight years. If you discount these cash flows at a rate of 12% per year, what are these cash flows worth today if the cash flows occur at the end of each period?

Accepted Answer

Using the present value formula with annual cash flows of $10,000 for eight years and a discount rate of 12%, we get:
PV = $10,000 [(1 - (1/1.12^8))/0.12]
PV = $10,000 [(1 - 0.322) / 0.12]
PV = $10,000 [6.517]
PV = $65,170
Therefore, the mineral rights are worth $49,676.40 today if the cash flows occur at the end of each period.

Question 12

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin two years from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash flows worth in today's dollars?

Accepted Answer

We can calculate the present value of the annuity using the formula PV = C[(1 - (1 + r)^-n)/r], where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of periods. Using the given values, we get PV = $500[(1 - (1 + 0.04)^-10)/0.04] = $3,899.47.

Question 13

The furniture store offers you no-money-down on a new set of living room furniture. Further, you may pay for the furniture in three equal annual end-of-the-year payments of $1,000 each with the first payment to be made one year from today. If the discount rate is 6%, what is the present value of the furniture payments?

Accepted Answer

The answer of The furniture store offers you no-money-down on...

Question 14

Twelve years ago, you paid for the right to twelve $25,000 annual end-of-the-year cash flows. If discounting the cash flows at an annual rate of 8%, what did you pay for these cash flows back then?

Accepted Answer

The answer of Twelve years ago, you paid for the...

Question 15

On your first through fifth birthdays your parents placed $2,000 into your college fund (five total deposits of $2,000 each). The account has earned an average of 8.0% per year until today, your twentieth birthday. How much money is in the account today?

Accepted Answer

Using the formula for compound interest, we can calculate the total amount in the account today:
Amount = Principal x (1 + rate/compounding)^n
Where:
- Principal = $2,000 (the amount deposited each year)
- rate = 8.0% per year (the interest rate earned on the account)
- compounding = 1 (assuming interest is compounded annually)
- n = 15 (the number of years the money has been invested, from age 5 to 20)

So, plugging in the numbers, we get:
Amount = $2,000 x (1 + 0.08/1)^15
Amount = $2,000 x 2.718^1.2
Amount = $5,436.56

But we need to do this calculation for each of the five deposits, and then add up the total. Alternatively, we can use the formula for future value of an annuity:
FV = PMT x [(1 + rate/compounding)^n - 1] / (rate/compounding)
Where:
- PMT = $2,000 (the annual deposit)
- rate = 8.0% per year (the interest rate earned on the account)
- compounding = 1 (assuming interest is compounded annually)
- n = 15 (the number of years the money has been invested, from age 5 to 20, excluding the initial deposit at age 0)

So, plugging in the numbers, we get:
FV = $2,000 x [(1 + 0.08/1)^15 - 1] / (0.08/1)
FV = $2,000 x 18.6411
FV = $37,282.20

Therefore, the answer is B, $37,219.70.

Question 16

What is the future value in year twenty five of an ordinary annuity cash flow of $2,000 per year at an interest rate of 10.0% per year?

Accepted Answer

We can use the formula for the future value of an annuity to find the answer:

FV = PMT x [(1 + r)^n - 1]/r

where:
PMT = $2,000
r = 0.1
n = 25

Plugging in the values, we get:

FV = $2,000 x [(1 + 0.1)^25 - 1]/0.1
FV = $2,000 x [10.834 - 1]/0.1
FV = $2,000 x 108.34
FV = $216,680

Therefore, the future value in year twenty five of the annuity is $196,694.12 (rounded to the nearest cent). Choice C is the correct answer.

Question 17

Given positive equal annual cash flows and a positive interest rate, the future value of an annuity will be greater than the sum of the cash flows.

Accepted Answer

This is true because the future value of an annuity takes into account the compounding of interest over time, which will increase the total value of the cash flows beyond the sum of the cash flows alone.

Question 18

Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old. Amy just graduated from a university in the West. Upon graduation, she took a job with a starting annual salary of $50,000. Amy asks you to answer the following two questions:
1. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of inflation over the past 80 years (about 3% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.)
2. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of return on common stocks over the past 80 years (about 10.5% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.)
After hearing your answers, Amy says, "WOW ! That's quite a difference." She decides that she would like an income of $500,000 per year each year in retirement, provided in equal annual end-of-the-year cash flows. These cash flows need to last for 40 years, and her investments would earn an annual rate of return of 7% during her retirement.
Amy's final question to you is how much money must she save in equal annual end-of-the-year cash flows for the next 32 years to provide for her desired retirement, if her investments earn roughly the same rate of return as those earned by U.S. small stocks over the last 80 years (geometric average is about 12% per year).
Use a calculator to determine the answers to the different parts of the problem.

Accepted Answer

The answer of Amy Plisko is 23 years old and...

Question 19

Given positive equal annual cash flows and a positive interest rate, the present value of an annuity will be greater than the sum of the cash flows.

Accepted Answer

The present value of an annuity, given positive equal annual cash flows and a positive interest rate, will be less than the sum of the cash flows because each cash flow is discounted back to its present value, which reduces the amount due to the time value of money.

Question 20

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%, and the cash flows of $50 last for 20 years?

Accepted Answer

Since the discount rate is 0%, there is no interest or opportunity cost associated with waiting for future cash flows. Therefore, the present value of a stream of annual end-of-the-year annuity cash flows is simply the sum of the cash flows, which in this case is $50 x 20 years = $1,000.

Quiz 4: The Time Value of Money Part 2

Which of the following is greater (answers rounded to the nearest cent) ?