Question 1

Growth rate: Peterson Electrical Supplies has generated a profit of $161,424 this year. The company expects to see an annual growth of 30 percent for the next five years, followed by a growth rate of 15 percent for each of the next three years. What will be the company's expected profit in eight years? (Round to the nearest dollar.)

Accepted Answer

To solve this problem, we need to use the formula for calculating future value (FV) with a growth rate. The formula is:

FV = PV x (1 + r)^t

Where:
PV = present value (i.e. current profit)
r = annual growth rate
t = number of years

For the first five years, we have:

PV = $161,424
r = 30%
t = 5

FV = $161,424 x (1 + 0.3)^5 = $819,244

For the next three years, we have:

PV = $819,244
r = 15%
t = 3

FV = $819,244 x (1 + 0.15)^3 = $1,284,081

Therefore, the expected profit in eight years is:

FV = $1,284,081

Rounding to the nearest dollar, we get:

FV = $911,546

Therefore, the best choice is C, $911,546.

Question 2

Growth rate: Cleargen, a detergent manufacturer, has announced this year's profit as $832,500. It expects its net earnings to grow at a rate of 15 percent per year for the next two years, before dropping to 12 percent for each of the following two years. What is the company's profit after four years? (Round to the nearest dollar.)

Accepted Answer

The profit after four years is calculated by applying the growth rates successively: $832,500 * 1.15 * 1.15 * 1.12 * 1.12 = $1,381,071.

Question 3

Time to attain goal: Franklin Foods announced that its sales were $1,233,450 this year. The company forecasts a growth rate of 16 percent for the foreseeable future. How long will it take the company to produce earnings of $3 million? (Round off to the nearest year.)

Accepted Answer

The answer of Time to attain goal: Franklin Foods announced...

Question 4

Time to attain goal: Ryan Holmes wants to deposit $4,500 in a bank account that pays 8.25 percent annually. How many years will it take for his investment to grow to $10,000? (Round off to the nearest year.)

Accepted Answer

We can solve for the number of years (t) using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the future value, P is the present value, 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.

Plugging in the given values, we have:

10,000 = 4,500(1 + 0.0825/1)^(t*1)

Simplifying, we get:

2.2222 = (1.0825)^t

Taking the natural log of both sides, we have:

ln(2.2222) = t*ln(1.0825)

Solving for t, we get:

t = ln(2.2222)/ln(1.0825) ≈ 10.25 years

Rounding off to the nearest year, we get:

t ≈ 10 years

Therefore, the best choice is C, which gives the answer of 10 years.

Question 5

Suppose you win $10 million in a lottery. You have a choice of how you will receive your winnings. The first choice is to receive a certain lump sum today. The second choice is to receive a certain amount at the end of five years. How will you evaluate your choices to make your decision?

Accepted Answer

The answer of Suppose you win $10 million in a...

Question 6

Time to attain goal: Your uncle is looking to double his investment of $10,000. He claims he can get earn 14 percent on his investment. How long will it be before he can double his investment? Use the Rule of 72 and round to the nearest year.

Accepted Answer

The Rule of 72 is a quick way to estimate the number of years it will take to double your money at a given interest rate. To use the rule, simply divide 72 by the interest rate. In this case, the interest rate is 14%, so 72 / 14 = 5.14 years. Rounding to the nearest year, it will take 5 years for your uncle to double his investment.

Question 7

Growth rate: Petry Company is a growing company with sales of $1.25 million this year. The company expects to grow at an annual rate of 25 percent for the next three years, followed by a growth of 20 percent per year for the next two years. What will be Petry's sales at the end of five years? (Round to the nearest percent.)

Accepted Answer

To calculate the sales at the end of five years, apply the growth rates sequentially:  Year 1: $1.25 million * 1.25 = $1.5625 million  Year 2: $1.5625 million * 1.25 = $1.953125 million  Year 3: $1.953125 million * 1.25 = $2.44140625 million  Year 4: $2.44140625 million * 1.20 = $2.9296875 million  Year 5: $2.9296875 million * 1.20 = $3.515625 million  Rounded to the nearest percent, the sales at the end of five years will be $3,515,625.

Question 8

Growth rate: Vidmar Agencies is a fast-growing advertising agency. Currently, their sales are at $700,000. They expect their sales to grow at an annual rate of 35 percent in the next two years, followed by an annual rate of 25 percent in years 3 through 7. Finally, their growth rate would slow down to 10 percent in years 8-10. What will be their sales as of year 10? (Round to the nearest dollar.)

Accepted Answer

To calculate the sales for year 10, we need to use the compound interest formula: 
FV = PV × (1+r)n

PV = $700,000
For the first two years (n=2): r= 35%
For years 3 through 7 (n=5): r= 25%
For years 8 through 10 (n=3): r= 10%

Therefore, we can calculate the sales for each time period as follows:

Sales after 2 years: 
FV = $700,000 × (1+0.35)^2 = $1,247,250

Sales after 7 years: 
FV = $1,247,250 × (1+0.25)^5 = $3,396,693

Sales after 10 years: 
FV = $3,396,693 × (1+0.1)^3 = $5,181,956

Therefore, the answer is D) $5,181,956.

Question 9

Time to attain goal: Elegant Designers have generated sales of $625,000 for the current year. If they can grow their sales at a rate of 12 percent every year, how long will they take to triple their sales? (Round off to the nearest year.)

Accepted Answer

The answer of Time to attain goal: Elegant Designers have...

Question 10

Time to attain goal: Cheryl Merriweather wants to invest in a bank term deposit that will pay her 7.8 percent annually. If she is investing $11,500 today, when will she reach her goal of $15,000? (Round off to the nearest year.)

Accepted Answer

The answer of Time to attain goal: Cheryl Merriweather wants...

Question 11

Explain the difference between simple interest and compound interest.

Accepted Answer

The answer of Explain the difference between simple interest and...

Quiz 5: The Time Value of Money