Question 1

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 Rule of 72 is indeed a rule of thumb for estimating the time it takes to double your money, by dividing 72 by the interest rate.

Question 2

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 is a convenient formula used to estimate the number of years it takes for an investment to double in value. It is calculated by dividing 72 by the annual rate of return. In this case, 72 divided by 8 equals 9, meaning it will take approximately 9 years for the investment to double in value. Over 45 years, the investment would have doubled about 5 times (since 45 divided by 9 equals 5), resulting in a final value of approximately $64,000.

Question 3

A manufacturer of Virtual Reality headsets has seen sales increase from 25,000 units per year to 100,000 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

The answer of A manufacturer of Virtual Reality headsets has...

Question 4

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 5

Your production manager informs you that currently the firm is producing 1,348 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)16.40 months
B)15.07 months
C)14 months
D)There is not enough information to answer this question.

Accepted Answer

The correct answer is A.The firm is currently producing 1,348 heating units per month and plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month.Let's call the number of months it will take to reach 3,000 units per month "t".We can use the formula for exponential growth to solve for t:A = P(1 + r)^twhere:A is the final amount (3,000 units per month)P is the initial amount (1,348 units per month)r is the annual growth rate (5%)t is the number of monthsPlugging in the values we know, we get:3,000 = 1,348(1 + 0.05)^tDividing both sides by 1,348, we get:2.225 = (1.05)^tTaking the logarithm of both sides, we get:log(2.225) = t * log(1.05)Solving for t, we get:t = log(2.225) / log(1.05) = 16.40 monthsTherefore, it will take the firm 16.40 months to reach 3,000 units per month.

Question 6

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 Rule of 72 is a simple way to estimate the number of years required to double the investment at a given annual rate of return. By dividing 72 by the number of years (72/9), you get an approximate annual rate of return of 8%.

Question 7

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 will take to double your money by dividing 72 by the interest rate. For example, if you have an interest rate of 6%, it will take approximately 12 years to double your money (72 ÷ 6 = 12).

Question 8

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 9

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 10

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 11

Antonio made $18,000 in the first movie he ever starred in.He 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 he 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

Antonio's salary for each movie can be calculated using the formula for geometric progression: $S_n = S_1 \times (1 + r)^{n-1}$, where $S_n$ is the salary for the nth movie, $S_1$ is the initial salary, $r$ is the rate of increase, and $n$ is the number of movies. Given $S_1 = 18,000$, $r = 46.18\% = 0.4618$, and $S_n = 5,350,000$, we solve for $n$:$5,350,000 = 18,000 \times (1 + 0.4618)^{n-1}$.Solving for $n$ gives approximately 15, indicating Antonio made 15 movies to earn $5,350,000 in a single movie.

Question 12

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 13

The dividends per share paid by Artisan Industries Inc.(AI)doubled from a starting value of $1.50 in 2010 to a value of $3.00 in 2016 (a six-year period).What was the approximate average annual rate of growth of AI'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 of an investment, divide 72 by the number of years it takes for the investment to double. In this case, AI's dividends doubled in six years, so the approximate annual rate of growth is 72 / 6 = 12%.

Question 14

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, then both discounting and compounding increase the future value of an investment and reduce its present value.

Question 15

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 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 basic principle of present value calculation in finance. Given the time period, interest rate, and future value, an individual can calculate the present value using formulas such as PV = FV/(1+r)^n.

Question 17

Lance has $3,500 but needs $7,000 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 Lance's account to grow to $7,000? Use the Rule of 72 to determine your answer. Note: The bicycle's price may have changed by the time Lance's account reaches a value of $7,000.
A)2 years
B)4 years
C)6 years
D)8 years

Accepted Answer

The answer of Lance has $3,500 but needs $7,000 to...

Question 18

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 well as interest rates. The formula is: number of years to double = 72/growth rate.

Question 19

In your first year out of college you hope to earn $30,000 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 14 years to reach an income level of $100,000 per year.
B)You would need to work for just over 10 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 5 years to reach an income level of $100,000 per year.

Accepted Answer

The Rule of 72 states that to determine the number of years it will take for an investment to double at a given annual rate of return, divide 72 by the annual rate of return. In this case, the annual rate of return is 10%, so it will take 72 / 10 = 7.2 years for the income to double to $60,000. It will then take another 7.2 years for the income to double again to $120,000. Therefore, it will take a total of 7.2 + 7.2 = 14.4 years to reach an income level of $120,000.

Question 20

Your father spent all of his adult life working in a small T-shirt making firm.His first year sales were $98,000 and his last year sales were $350,000.If the firm grew at an average rate of 3.35% per year,how many years did your father sell T-shirts at his firm?
A)43.16 years
B)40.00 years
C)38.63 years
D)25.91 years

Accepted Answer

Let the number of years your father sold T-shirts be n.
We know that his first year sales were $98,000 and his last year sales were $350,000.
The growth rate per year is 3.35%. Therefore, the sales at the end of n years can be given by:
98000 * (1 + 0.0335)^n = 350000
Simplifying this equation, we get:
(1 + 0.0335)^n = 3.5714
Taking logarithm on both sides, we get:
n * log(1 + 0.0335) = log(3.5714)
n = log(3.5714) / log(1 + 0.0335)
n = 38.63 years (approx.)
Therefore, the best choice is C, 38.63 years.

Quiz 3: The Time Value of Money Part 1

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

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.

A manufacturer of Virtual Reality headsets has seen sales increase from 25,000 units per year to 100,000 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.

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.

Your production manager informs you that currently the firm is producing 1,348 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?

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.

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

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

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.

Antonio made $18,000 in the first movie he ever starred in.He 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 he make in order to earn $5,350,000 in a single movie?

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?

The dividends per share paid by Artisan Industries Inc.(AI) doubled from a starting value of $1.50 in 2010 to a value of $3.00 in 2016 (a six-year period) .What was the approximate average annual rate of growth of AI's dividends per share? Use the Rule of 72 to determine your answer.

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

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.

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

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.

In your first year out of college you hope to earn $30,000 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.

Your father spent all of his adult life working in a small T-shirt making firm.His first year sales were $98,000 and his last year sales were $350,000.If the firm grew at an average rate of 3.35% per year,how many years did your father sell T-shirts at his firm?