Question 1

You currently have $3,500 invested at an annual rate of 8%.How long will it take for this investment to grow to a value of $5,000?

Accepted Answer

We can use the formula for compound interest to solve this problem:

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

Where:
A = final amount ($5,000)
P = initial amount ($3,500)
r = annual interest rate (8%)
n = number of times compounded per year (assuming annually, n = 1)
t = time (in years)

Plugging in the values, we get:

$5,000 = $3,500(1 + 0.08/1)^(1t)

Simplifying:

1.4286 = (1.08)^t

Taking the logarithm of both sides:

log(1.4286) = t log(1.08)

t = log(1.4286) / log(1.08)

t ≈ 4.63 years

Therefore, the best choice is A, 4.63 years.

Question 2

Even if you are given a present value,a single future value,and a time period,solving for the rate of return,r,is still a trial-and-error process.

Accepted Answer

The rate of return can be calculated using the formula for compound interest or the present value formula, which allows for direct computation without trial-and-error.

Question 3

Upon taking his first job out of college,your Dad earned an annual salary of $33,000 and set a goal to earn $100,000 per year.If his salary increased at an average annual rate of 5.5%,how long did it take to reach his goal?

Accepted Answer

To find out how long it takes for the salary to grow from $33,000 to $100,000 with an annual growth rate of 5.5%, we use the formula for exponential growth: $A = P(1 + r)^t$, where $A$ is the amount we're solving for ($100,000), $P$ is the initial amount ($33,000), $r$ is the rate of growth (5.5%, or 0.055 when expressed as a decimal), and $t$ is the time in years. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{\log(1 + r)}$. Plugging in the numbers, $t = \frac{\log(100,000/33,000)}{\log(1 + 0.055)}$, which calculates to approximately 20.71 years.

Question 4

The question "What is the current value of an amount of cash that will be received at a specific time in the future?" is best answered by which form of the TVM equation?

Accepted Answer

The correct formula for calculating the present value (PV) of a future amount of cash (FV) that will be received at a specific time in the future, given a specific rate (r) and number of periods (n), is PV = $\frac { FV } { ( 1 + r ) ^ { n } }$. This formula discounts the future value back to its present value.

Question 5

Dividend growth rate is important to many investors.You are considering investing in a firm after looking at the firm's dividends over a six-year period.At the end of the year 2010,the firm paid a dividend of $0.98.At year-end 2016,it paid a dividend of $1.64.What was the average annual growth rate of dividends for this firm?

Accepted Answer

The average annual growth rate can be calculated using the formula for compound annual growth rate (CAGR): CAGR = (Ending Value/Beginning Value)^(1/Number of Years) - 1. Using the given values: CAGR = ($1.64/$0.98)^(1/6) - 1 = 8.96%.

Question 6

The question "At what rate is my money growing over time?" is best answered by which form of the TVM equation?

Accepted Answer

The correct choice is C, r = (FV/PV)^(1/n) - 1, because it directly calculates the rate (r) at which money grows over time, given the future value (FV), present value (PV), and the number of periods (n).

Question 7

Other things remaining equal,the price today and the growth rate are inversely related.

Accepted Answer

This is because as the growth rate increases, the expected future cash flows of the investment also increase, which in turn increases the present value of the investment and therefore its price. Conversely, as the growth rate decreases, the present value and price of the investment also decrease.

Question 8

The question "How long will I have to wait to reach a certain future value?" is best answered by which form of the TVM equation?

Accepted Answer

The correct formula for calculating the number of periods (n) required to reach a certain future value (FV) given a present value (PV) and a constant rate of return (r) is D) $n = \frac { \ln ( \mathrm { FV } / \mathrm { PV } ) } { \ln ( 1 + \mathrm { r } ) }$. This formula rearranges the basic future value formula to solve for the time period, using logarithms to isolate n.

Question 9

Your grandfather likes to tell the story about how he started his ranch with 100 head of cattle and grew the ranch to 2,500 head of cattle.He said "My plan was simple: grow the number of head of cattle at a rate of 10% per year." Your grandfather reached his goal before he retired.How long did it take him?

Accepted Answer

To solve this problem, we need to use the formula for compound interest:

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

where:
A = final amount
P = principal amount (the initial number of head of cattle)
r = annual interest rate (in this case, 10%)
n = number of times the interest is compounded per year (assuming annual compounding, n = 1)
t = time in years

We are trying to find t, so we can rearrange the formula to solve for t:

t = (ln(A/P))/(n * ln(1 + r/n))

Plugging in the numbers from the problem, we get:

t = (ln(2500/100))/(1 * ln(1 + 0.1/1))
t = (ln(25))/(ln(1.1))
t = 31.43 years (rounded to two decimal places)

Therefore, the answer is C) 31.43 years.

Question 10

You gave your little sister two rabbits for Easter three years ago and now she has 64 of the cute little bunnies.What is the average annual rate of increase in the number of rabbits your sister owns? Note: Your parents are not very pleased with you right now.

Accepted Answer

The average annual rate of increase can be calculated using the formula for the average annual growth rate (AAGR), which is [(Ending value/Beginning value)^(1/Number of years)] - 1. In this case, the beginning value is 2 rabbits, the ending value is 64 rabbits, and the time period is 3 years. Plugging these values into the formula gives us [(64/2)^(1/3)] - 1 = 3.1748 - 1 = 2.1748, or 217.5% as the average annual rate of increase.

Question 11

Even if you are given a present value,a future value,and an interest rate,solving for the time period "n" is still a trial-and-error process.

Accepted Answer

The time period "n" can be solved algebraically using the formula for present value or future value when the interest rate and either the present or future value are known, eliminating the need for a trial-and-error process.

Question 12

You have just won the university lottery.If you graduate,you will receive a refund equal to the amount of tuition you paid in your first four years of school.However,you need money now and a firm that specializes in buying expected future cash flows has offered to discount the lottery winnings at a rate of 8% and pay you cash today in exchange for your future lottery winnings.Since you have studied finance,you insist that they discount the cash flows at 12% instead of 8% because there is some risk as to the certainty of your graduating.If the firm agrees to your demand,then this means they will increase the present value of what they will pay you today.

Accepted Answer

The statement is incorrect. If the firm agrees to discount the cash flows at a higher rate of 12%, it will decrease the present value of what they will pay you today as the higher discount rate means a lower present value.

Question 13

Family Construction had sales three years ago of $2,150,000.This year their sales hit $2,900,000.What has been the firm's average annual rate of growth of sales?

Accepted Answer

To calculate the average annual rate of growth of sales, we use the formula: ((Ending value / Beginning value)^(1/number of years)) - 1

Plugging in the values, we get: 
((2,900,000 / 2,150,000)^(1/3)) - 1 = 0.1049 or 10.49%

Therefore, the correct answer is B.

Question 14

At your birth,your grandparents put $5,000 into a college fund for you.Now you want to use the fund to pay your first year of college costs of $23,000.To have enough money in your college fund for your stated purpose,what annual rate of return would have to have been earned on the account over an 18-year period?

Accepted Answer

The answer of At your birth,your grandparents put $5,000 into...

Question 15

Current annual dividends for Simpsons Frozen Foods Inc.,are $1.35 per share.Four years ago,dividends per share were exactly $1.00.What has been the rate of growth for Simpsons' dividends per share?

Accepted Answer

The answer of Current annual dividends for Simpsons Frozen Foods...

Question 16

Five years ago,Maria's annual salary was $73,500.Today,she earns $91,900.What has been the average annual percentage rate of growth of Maria's salary?

Accepted Answer

The answer of Five years ago,Maria's annual salary was $73,500.Today,she...

Question 17

Drew is taking over as Chief Marketing Officer at SouthWest Foods.She has pledged to increase sales from their current level of $8,000,000 at a rate of 11% per year until the firm hits sales of $15,000,000 per year.How long will it take the firm to hit the target goal at this rate of increase?

Accepted Answer

The answer of Drew is taking over as Chief Marketing...

Question 18

Consider the TVM equation: the variable "r" may be defined as the discount rate or the growth rate depending upon how the equation is being used.

Accepted Answer

The variable "r" in the TVM equation can be defined as the discount rate or the growth rate depending on how the equation is being used. For example, when calculating the present value of a future cash flow, "r" would represent the discount rate. However, when calculating the future value of an investment, "r" would represent the growth rate.

Question 19

The Johnstown School District had 3,171 students enrolled four years ago.Today,the district enrollment is 2,618 students.What has been the annual rate of change of student enrollment in the School District over this time period?

Accepted Answer

The answer of The Johnstown School District had 3,171 students...

Question 20

You have saved $1,250 for a used motorcycle that has a current price of $1,550.If your money is sitting in an account earning 2.25% per year,how long will it take for this account to grow to $1,550? Note: The motorcycle's price may have changed by the time your account reaches a value of $1,550.

Accepted Answer

The answer of You have saved $1,250 for a used...

Quiz 3: The Time Value of Money Part 1