Chapter 4 Smartbook

If you want to double your money in five years, what is the approximate annual rate of return you must earn using the Rule of 72?

14.4 percent Reason: 72/5 = 14.4 percent

Ten years ago, Alicia invested $9,000 at 5 percent interest. How much more money would she have today if she had invested the money at 6 percent instead of 5 percent? Interest is compounded annually.

$1,457.58 Reason: FV = $9,000 × (1 + 0.05)10 = $14,660.05 FV = $9,000 × (1 + 0.06)10 = $16,117.63 Difference = $16,117.63 - $14,660.05 = $1,457.58

What is the value today of $2,500 to be received in 7 years if the discount rate is 3.5 percent?

$1,964.98 Reason: PV = $2,500/(1 + 0.035)^7 = $1,964.98

Which one of these formulas illustrates the compounding of interest?

$100 × (1 + 0.06) × (1 + 0.06)

Louisa invested $12,000 in a business venture which returned $4,000, $6,000, and $8,000 over the past three years. Which of these amounts is (are) cash outflows to Louisa?

$12,000 investment

This morning, Mal Reynolds invested $1,000 for 40 years. He will earn 15% interest for the first twenty five years and 10% interest for the last fifteen years. How much will his investment be worth 40 years from now?

$137,511 Reason: FV = $1,000 × (1 + 0.15)^25 × (1 + 0.10)^15 = $137,511

Five years ago, Lewis Equipment purchased equipment costing $212,000. Two years ago, the firm paid $32,000 for updates to that equipment. This year, the firm sold the equipment for $189,000. Which of these cash flows is (are) cash inflows to Lewis Equipment?

$189,000 sale price

A bank loaned money at 7 percent interest for five years to Stu. The loan will be repaid in one lump sum payment of $3,366.12. How much did Stu borrow?

$2,400 Reason: PV = $3,366.12/(1 + 0.07)^5 = $2,400

Five years ago, Alicia invested $10,000 at 5% interest. How much less money would she have today if she had invested the money at 4% instead of 5%? Interest is compounded annually.

$596 Reason: FV = $10,000 × (1 + 0.05)5 = $12,763 FV = $10,000 × (1 + 0.04)5 = $12,167 Difference = $12,167 - $12,763 = -$596

This morning, Kurt invested $500 for five years. He will earn 3 percent interest for the first two years and 5 percent interest for the last three years. How much will his investment be worth 5 years from now?

$614.06 Reason: FV = $500 × (1 + 0.03)^2 × (1 + 0.05)^3 = $614.06

You expect to receive a gift of $1,000 five years from today. What is the value of this gift today if the discount rates are 8% for the next three years and 10% for the next two years?

$656.06 Reason: PV = $1,000/[(1 + 0.08)^3 × (1 + 0.10)^2] = $656.06

Susette invested $10,000 twenty years ago. Ten years ago, she invested an additional $5,000. Last year, she withdrew $8,000 to pay for a vacation. If you were to draw a time line of these events, which value(s) would be treated as a cash inflow(s) to Susette?

$8,000 cash withdrawal

You expect to receive a gift of $1,000 three years from today. What is the value of this gift today if the discount rates are 6 percent, 6.5 percent, and 7 percent for the next three years, respectively?

$827.87 Reason: PV = $1,000/[(1 + 0.06) × (1 + 0.065) × (1 + 0.07)] = $827.87

Solving which of the following problems illustrates discounting? Select all that apply.

- How much do you need to invest today at 7 percent interest to have $40,000 available for college expenses in 17 years? - What is a $1,000 gift to be received next year worth today if the interest rate is 5 percent?

$100 represents the present value, as it is used in the present value formula, for which of these problems? Select all that apply.

- Russ' savings account increased in value from $100 five years ago to $111 today. - Janice invested $100 today at 9 percent interest for ten years.

Which of these statements is (are) correct? Assume a constant, positive, annual rate of interest. Select all that apply.

- The longer the time period, the greater the future value of a stated sum. - The shorter the time period, the higher the present value of a stated future value.

Ten years ago, you put $5,000 in a savings account. Today, your investment has the purchasing power of $4,800 What is your real rate of return? (just calculate like a normal interest rate)

-0.41%

Approximately how long will it take a $2,500 investment to grow to $5,000 at an interest rate of 6 percent?

12 years Reason: 72/6 = 12 years

How long will it take to increase a $2,200 investment to $10,000 if the interest rate is 6.5 percent?

24.04 years Reason: Using a financial calculator: I = 6.5; PV = -2,200; PMT = 0; FV = 10,000

Twelve years ago, you invested $4,800. Today, your investment is worth $8,750. What is your rate of return?

5.13 percent Reason: i = ($8,750/$4,800)^1/12 - 1 = 5.13 percent

How long will it take to double a $2,000 investment at 10% interest

7.27 years Reason: Using a financial calculator: I = 10; PV = -2,000; PMT = 0; FV = 4,000

Which one of these formulas correctly defines the Rule of 72?

Approximate number of years to double money × Interest rate = 72

Which one of these correctly defines the future value of a $1,000 investment?

Future value is the value of the investment at any date after the initial investment date.

Alicia invested $1,000 three years ago at a fixed rate of 5 percent interest. Which one of these illustrates the compounding of interest on this investment?

Alicia's investment was worth $1,050 after one year and $1,102.50 after two years.

Which one of these statements is correct concerning the relationship of PV, FV, i, and N? Assume the interest rate is constant and positive.

All else held constant, the longer the time period, the lower the present value.

Which one of the following best illustrates simple interest?

Ann has a $1,000 savings account that will pay her $40 of interest each year for five years.

Four years ago, AB Tools had an extra $1100 it did not currently need so the firm deposited the $1100 in a new savings account. Three years ago, the firm withdrew $300. Last year, the firm deposited $800 into the account. Today, the account is worth $1,600 and the firm is withdrawing the entire balance. Which statement correctly defines a portion of the time line for the account?

At time zero, there is a cash outflow of $1100.

Four years ago, AB Tools had an extra $500 it did not currently need so the firm deposited the $500 in a new savings account. Three years ago, the firm withdrew $200. Last year, the firm deposited $800 into the account. Today, the account is worth $1,180 and the firm is withdrawing the entire balance. Which statement correctly defines a portion of the time line for the account if the $500 deposit is shown at time zero?

At year 1, there is a cash inflow of $200.

Which one of these cash flows best illustrates a cash outflow?

Better Bakery purchased a new oven for $28,600.

Which term is defined as the process of finding a present value by reducing a future value using the applicable rates of interest?

Discounting

Which formula computes the value in year 9 of a $10,000 investment in year 2 if the interest rate is 6 percent?

FV = $10,000 × (1 + 0.06)^7

Which formula illustrates the value of $100 invested for one year at 5 percent interest?

FV = $100 × (1 + 0.05)

How is the future value of $500 invested for one year at 6 percent annual interest computed?

FV = $500 × (1 + 0.06)^1

Which formula moves a cash flow of $800 ahead six years in time at an interest rate of 5 percent?

FV = $800 × (1 + 0.05)^6

How is future value best defined?

Future value is the value of an investment after one or more periods.

Which one of these statements is correct concerning the relationship of i to PV, FV, and N?

If you increase the interest rate, all else held constant, the future value will increase.

Today, both Marti and Neil invested $5,000. Marti's investment will return 4 percent while Neil's will return 8 percent. Both rates will be compounded. Which one of these statements is correct?

Neil's investment will increase in value faster than Marti's.

Charity House has been promised a $25,000 donation five years from today. How much would that gift be worth next year? Assume an interest rate of 8 percent.

PV = $25,000/(1 + 0.08)^4

Which one of the following is the correct application of the present value formula for this problem: Maria expects to receive $5,000 from her grandmother upon her graduation in three years. What is the current value of this gift if the interest rate is 4 percent?

PV = $5,000/(1 + 0.04)^3

You expect to receive a gift of $5,000 six years from today. Which formula provides the value of this gift two years from today if the discount rate is 9 percent?

PV = $5,000/(1 + 0.09)^4

Which of these statements correctly defines the Rule of 72?

The Rule of 72 provides an approximation of the number of years needed to double your money given a particular rate of interest.

A project has these cash flows: $2,000 3 years ago, $1,000 now and -$2,000 three years from now. Which is the correct formula for computing today's value of these cash flows given a 6% rate of interest?

Today's value = $2,000 × (1 + 0.06)^3 + $1,000 × (1 + 0.06)^0 - $2,000/(1 + 0.06)^3

A project has these cash flows: -$2,000 two years ago, $800 one year ago, and $1,200 one year from now. Which is the correct formula for computing today's value of these cash flows given a 6 percent rate of interest?

Today's value = -$2,000 × (1 + 0.06)^2 + $800 × (1 + 0.06) + $1,200/(1 + 0.06)

You invested $1,000 and lost 21 percent of that value during the first year. Which formula computes the rate needed to increase your investment back to $1,000 by the end of the second year?

i = $1,000/[$1,000 × (1 - 0.21)]^1/1 - 1

Sara invested $3,400 six years ago. Today, her investment is worth $4,200. Which formula will correctly compute her rate of return?

i = ($4,200/$3,400)^1/6 - 1

Which of these is the correct formula for computing the interest rate on an investment?

i = (FVsubN/PV)^1/N - 1

Two years ago, your investments were worth $11,000. Today, those same investments are only worth $9,800, for an annual loss of 5.61 percent. How do you compute the return needed to increase your investments to $11,000 in the next two years?

i= ($11,000/$9,800)^1/2 - 1

In the case of simple interest, interest is applied each period to

the principal only