Question 1

The Rule of 72 can be used to quickly estimate interest rates necessary to double your money in a given time period without the use of a spreadsheet or calculator.However,the rule does NOT work for estimating growth rates.

Accepted Answer

The Rule of 72 can be used to estimate growth rates as it is a simple mathematical formula that helps in approximating the number of years it takes to double the value of an investment.

Question 2

If college tuition and fees increase at an annual rate of 7% per year,and your little sister is currently starting her freshman year in high school,what is the expected cost of her first year of college in four years if tuition and fees are currently $6,850 per year? How much for the start of her senior year of college starting three years after that?

Accepted Answer

The answer of If college tuition and fees increase at...

Question 3

A manufacturer of LCD televisions has seen sales increase from 125,000 units per year to 500,000 units per year in 8 years.What has been the firm's average annual rate of increase in the number of television sets sold? Use the Rule of 72 to determine your answer.
A)The average annual rate of change has been between 10% and 11%.
B)The average annual rate of change has been between 18% and 19%.
C)The average annual rate of change has been between 15% and 16%.
D)There is not enough information to answer this question.

Accepted Answer

To find the average annual rate of increase we use the formula:
[(Ending Value / Beginning Value)^(1/# of years) - 1] * 100

Plugging in the values we get:
[(500,000 / 125,000)^(1/8) - 1] * 100 ≈ 18.47%

Using the Rule of 72, we can estimate how long it will take for the sales to double. 
72 / 18.47 ≈ 3.89 years

Since these values fall between 18% and 19%, the best choice is B.

Question 4

Your production manager informs you that currently the firm is producing 1,438 heating units per month but has plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month.How many months will this take?
A)27.33 months
B)15.07 months
C)14 months
D)There is not enough information to answer this question.

Accepted Answer

To find the number of months required, use the formula for exponential growth: Final amount = Initial amount * (1 + growth rate)^number of periods. Solving 3000 = 1438 * (1.05)^n gives n ≈ 15.07 months.

Question 5

Kelvin has $2,500 but needs $5,000 to purchase a new golf cart.If he can invest his money at a rate of 12% per year,approximately how many years will it take the money in Kelvin's account to grow to $5,000? Use the Rule of 72 to determine your answer. Note: The golf cart's price may have changed by the time Kelvin's account reaches a value of $5,000.
A)2 years
B)4 years
C)6 years
D)8 years

Accepted Answer

The Rule of 72 is a simple way to estimate the number of years required to double an investment at a fixed annual rate of interest. By dividing 72 by the annual interest rate (12%), we get 6 years for the investment to double from $2,500 to $5,000.

Question 6

In your first year out of college you hope to earn $60,000 per year.How many years will you have to work until you earn $120,000 if your income increases at a rate of 10% per year? Use the Rule of 72 to determine your answer.
A)You would need to work for just over 5 years to reach an income level of $100,000 per year.
B)You would need to work for just over 6 years to reach an income level of $100,000 per year.
C)You would need to work for just over 7 years to reach an income level of $100,000 per year.
D)You would need to work for just over 8 years to reach an income level of $100,000 per year.

Accepted Answer

The Rule of 72 estimates the number of years required to double an investment at a fixed annual rate of interest. By dividing 72 by the annual increase rate (10%), you get approximately 7.2 years to double the income from $60,000 to $120,000.

Question 7

Dan Preston made $18,000 in the first movie he ever starred in.Dan soon made more and more movies and more and more money.At a 46.18% rate of salary increase per movie,how many movies did Dan make in order to earn $5,350,000 in a single movie?
A)84 movies
B)34 movies
C)22 movies
D)15 movies

Accepted Answer

The answer of Dan Preston made $18,000 in the first...

Question 8

What annual rate of return must you earn to double your money in about 9 years? Use the Rule of 72 to determine your answer.
A)You would need to earn an annual rate of return of about 12%.
B)You would need to earn an annual rate of return of about 10%.
C)You would need to earn an annual rate of return of about 8%.
D)There is not enough information to answer this question.

Accepted Answer

The answer of What annual rate of return must you...

Question 9

You have $5,000 in an index mutual fund.At an average annual rate of return of 10% per year,this investment should exceed a value of $500,000 by the time you retire in 40 years.

Accepted Answer

Using the formula for compound interest, $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount ($5,000), $r$ is the annual interest rate (10% or 0.10), $n$ is the number of times that interest is compounded per year (assuming annually, so 1), and $t$ is the time the money is invested for (40 years), the calculation would be $A = 5000(1 + \frac{0.10}{1})^{1*40}$. This does not exceed $500,000, but rather results in an amount significantly less than that, demonstrating that the statement is false.

Question 10

The Rule of 72 is a rule of thumb for estimating the length of time necessary to double your money,given an interest rate.

Accepted Answer

The statement is true. The Rule of 72 states that you can estimate the time it takes for your money to double by dividing 72 by the interest rate.

Question 11

The Rule of 72 is a rule of thumb for estimating the interest rate necessary to double your money,given a period of time.

Accepted Answer

The Rule of 72 states that you can estimate the number of years it takes to double your money by dividing the interest rate (in percentage) by 72.

Question 12

The dividends per share paid by Fantastically Fine Ferns Inc.(FFF)doubled from a starting value of $1.50 in 2007 to a value of $3.00 in 2013 (a six-year period).What was the approximate average annual rate of growth of FFF's dividends per share? Use the Rule of 72 to determine your answer.
A)FFF's dividends grew at an annual rate of approximately 12% per year.
B)FFF's dividends grew at an annual rate of approximately 10% per year.
C)FFF's dividends grew at an annual rate of approximately 8% per year.
D)FFF's dividends grew at an annual rate of approximately 6% per year.

Accepted Answer

The Rule of 72 states that to find the approximate annual rate of growth, divide 72 by the number of years it takes for the value to double. In this case, it took 6 years for the dividends to double, so the approximate annual rate of growth is 72 / 6 = 12%.

Question 13

Your father spent all of his adult life working in a small T-shirt making firm.His first year of sales was $118,000 and his last year of sales was $450,000.If the firm grew at an average rate of 3.15% per year,how many years did your father sell T-shirts at his firm?
A)43.16 years
B)40.00 years
C)31.68 years
D)25.91 years

Accepted Answer

The correct answer is A.The formula for compound interest is:A = P(1 + r/n)^(nt)where:A is the final amountP is the principal (initial amount)r is the annual interest raten is the number of times per year that the interest is compoundedt is the number of yearsIn this case, we have:P = $118,000A = $450,000r = 3.15% = 0.0315n = 1 (compounded annually)t = ?Solving for t, we get:t = log(A/P) / log(1 + r/n)t = log(450000/118000) / log(1 + 0.0315/1)t = 43.16 yearsTherefore, your father sold T-shirts at his firm for 43.16 years.

Question 14

You win the $5,000,000 lottery that pays you $250,000 per year over a 20-year period.Given negative interest rates,the lottery has a present value that is less than $5,000,000.

Accepted Answer

With negative interest rates, the present value of the lottery winnings would actually be more than $5,000,000 because the future payments are worth more in today's dollars when discounted at a negative rate.

Question 15

You can invest your money at a rate of 7% per year.At this rate it will take you just over ________ years to double your money.Use the Rule of 72 to determine your answer.
A)4
B)10
C)5.5
D)There is not enough information to answer this question.

Accepted Answer

The Rule of 72 is a simple way to estimate the number of years required to double an investment at a given annual rate of return. By dividing 72 by the annual rate of return, you get an approximate number of years. In this case, 72 divided by 7 equals approximately 10.3 years, so the closest answer is 10 years.

Question 16

Given a time period,an interest rate,and a future value,a person could solve for a present value.

Accepted Answer

This is the formula for Present Value: 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 time periods. Given any three of these variables, a person could solve for the missing fourth variable.

Question 17

If interest rates are positive,then discounting increases the future value of an investment while compounding reduces the present value of an investment.

Accepted Answer

If interest rates are positive, compounding increases the future value of an investment while discounting reduces the present value of an investment.

Question 18

Given enough time,you could double your money with a risk-free investment.

Accepted Answer

Given enough time and assuming a positive interest rate, even a small rate of return on a risk-free investment (like government bonds) can compound, eventually doubling the initial investment.

Question 19

A plant nursery pays $2,000 for 800 one-gallon flowering trees,plants them,and forgets them.Five years later,the nursery is able to sell each of the 100 trees that survived for $50 each.What is the rate of return on its total investment?

Accepted Answer

The answer of A plant nursery pays $2,000 for 800...

Question 20

Assume you put $2,000 into a tax-free investment and leave it there for 45 years at an annual rate of 8%.According to the Rule of 72,your investment will grow to a value of about $64,000.

Accepted Answer

The Rule of 72 states that you can estimate the time it takes for an investment to double by dividing 72 by the annual rate of return. In this case, 72 divided by 8 equals 9. Therefore, your investment will double approximately every 9 years. After 45 years, it will have doubled 5 times (45 divided by 9 equals 5), bringing the value to approximately $32,000 for each doubling. Therefore, the investment will be worth approximately $64,000.

Quiz 3: The Time Value of Money Part 1

The Rule of 72 can be used to quickly estimate interest rates necessary to double your money in a given time period without the use of a spreadsheet or calculator.However,the rule does NOT work for estimating growth rates.

A manufacturer of LCD televisions has seen sales increase from 125,000 units per year to 500,000 units per year in 8 years.What has been the firm's average annual rate of increase in the number of television sets sold? Use the Rule of 72 to determine your answer.

Your production manager informs you that currently the firm is producing 1,438 heating units per month but has plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month.How many months will this take?

In your first year out of college you hope to earn $60,000 per year.How many years will you have to work until you earn $120,000 if your income increases at a rate of 10% per year? Use the Rule of 72 to determine your answer.

Dan Preston made $18,000 in the first movie he ever starred in.Dan soon made more and more movies and more and more money.At a 46.18% rate of salary increase per movie,how many movies did Dan make in order to earn $5,350,000 in a single movie?

What annual rate of return must you earn to double your money in about 9 years? Use the Rule of 72 to determine your answer.