Question 1

Granny puts $35,000 into a bank account earning 4%. You can't withdraw the money until the balance has doubled. How long will you have to leave the money in the account?

Accepted Answer

To figure out how long it will take for the balance to double, we need to use the formula for compound interest:

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

where:

A = the ending balance (in this case, $70,000)
P = the principal (the initial amount put into the account, $35,000)
r = the annual interest rate (4%, or 0.04 as a decimal)
n = the number of times the interest is compounded per year (we'll assume it's compounded annually, so n = 1)
t = the time (in years) that the money is left in the account

We want to solve for t, so we'll rearrange the formula:

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

Plugging in the values we know:

t = [ln(2)] / [(1 * ln(1 + 0.04/1)]
t = [0.693147... / 0.040000...]
t ≈ 17.328
t ≈ 18 (rounded up to the nearest whole year)

Therefore, Granny will need to leave the money in the account for 18 years to double the balance, so the best choice is C) 18 years.

Question 2

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its ﬁrst year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of
Year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total
Restaurants.
Between the end of year 2 and the end of year 3, the number of eating establishments grew at a
Rate of _________ compounded annually.

Accepted Answer

The answer of Chia Burgers began operations by opening 115...

Question 3

Koji invested $3,300 at 7.75% interest. After a period of time he withdrew $9,383.31. How long did Koji have his money invested?

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, since the interest rate is given as an annual rate and there's no indication that it's compounded more frequently than once a year, we can simplify the formula to A = P(1 + r)^t. We're given that A = $9,383.31, P = $3,300, and r = 7.75% or 0.0775 in decimal form. We need to solve for t. Rearranging the formula to solve for t gives us t = log(A/P) / log(1 + r). Plugging in the numbers gives us t = log(9383.31/3300) / log(1 + 0.0775), which calculates to approximately 14 years.

Question 4

Sampson, Inc. invested $1.325 million in a project that earned an 8.25% rate of return. Sampson sold their investment for $3,713,459. How much sooner could Sampson have sold the company if
They only wanted $3 million from the project?

Accepted Answer

First, we need to find out how long it took for the project to earn $3,713,459:

PV + I = FV

where PV is the initial investment, I is the interest earned, and FV is the final value.

$1.325m + I = $3,713,459

I = $2,388,459

Now we can use the formula for the future value of an annuity to find out how long it would take for the project to reach $3 million:

FV = CF x [(1 + r)^n - 1] / r

where CF is the cash flow, r is the interest rate, and n is the number of periods.

$3m = CF x [(1 + 0.0825)^n - 1] / 0.0825

$2,388,459 = CF x [(1 + 0.0825)^n - 1]

CF = $226,496.60

$3m / $226,496.60 = 13.25

So it would take 13.25 periods to reach $3 million. Since the project earned an 8.25% rate of return, each period is equal to one year.

13.25 - 4 = 9.25

Therefore, Sampson could have sold the company 9.25 years sooner if they only wanted $3 million from the project. Rounded to the nearest year, the answer is 9. Answer choice A is the closest.

Question 5

In 1889, Vincent Van Gogh's painting, "Sunﬂowers," sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you,
What annual return on investment would your family have earned on the painting?

Accepted Answer

The answer of In 1889, Vincent Van Gogh's painting, "Sunﬂowers,"...

Question 6

At a 6% rate of interest you will double your money in approximately ___ years.

Accepted Answer

In order to double your money at a 6% rate of interest, you would need to use the Rule of 72. The Rule of 72 states that you divide 72 by the annual interest rate to get the approximate number of years it takes for your investment to double. So, 72 divided by 6 is 12. Thus, your money will double in approximately 12 years at a 6% rate of interest.

Question 7

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its ﬁrst year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of
Year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total
Restaurants.
If, over the next ﬁve years, eating establishments are expected to grow at the annual growth rate as
They did during years 1 to 5, forecast the number of eating establishments at the end of year 10.

Accepted Answer

The growth from year 1 to year 5 is from 115 to 138 restaurants, which is an increase of 23 restaurants over 4 years. The average annual growth rate is 23/4 = 5.75 restaurants per year. Over the next 5 years, this growth rate would add 5.75 * 5 = 28.75 restaurants to the 138 existing ones, resulting in approximately 167.75, which rounds to 172.

Question 8

An investor deposited $10,500 in an account. At the end of year four, the account had accumulated $5,728.88. Over the ﬁrst four years, the account earned ________ compounded annually.

Accepted Answer

The formula for compound interest is A = P(1 + r)^n. Here, A = $5,728.88, P = $10,500, and n = 4. Solving for r gives an annual interest rate of approximately 11.5%.

Question 9

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its ﬁrst year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of
Year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total
Restaurants.
From the end of year 1 to the end of year 5, the number of eating establishments grew at a rate of
____________ compounded annually.

Accepted Answer

The answer of Chia Burgers began operations by opening 115...

Question 10

Moe and Joe are twins. Moe invested $1,000, earned 9% annually, and now has $1,992.56. Joe invested $1,000, earned 6.47%, and now has $1,992.97. Joe invested his money _____ years
Before Moe.

Accepted Answer

The correct answer is C.Moe's investment earned 9% annually, and he now has $1,992.56. This means that he has earned $992.56 in interest.Joe's investment earned 6.47% annually, and he now has $1,992.97. This means that he has earned $992.97 in interest.Since Moe has earned more interest than Joe, he must have invested his money for a longer period of time.To find out how many years longer Moe invested his money for, we can use the following formula:Interest = Principal * Rate * TimeFor Moe, we have:$992.56 = $1,000 * 9% * TimeSolving for Time, we get:Time = 11 yearsFor Joe, we have:$992.97 = $1,000 * 6.47% * TimeSolving for Time, we get:Time = 14 yearsTherefore, Moe invested his money for 14 - 11 = 3 years longer than Joe.

Question 11

Alpha, Inc. is saving money to build a new factory. Six years ago they set aside $250,000 for this purpose. Today, that account is worth $306,958. What rate of interest is Alpha earning on this
Money?

Accepted Answer

The answer of Alpha, Inc. is saving money to build...

Question 12

At a 3% rate of interest, you will quadruple your money in approximately ____ years.

Accepted Answer

To quadruple your money, you need it to grow to 4 times its original amount. Using the rule of 72, which is a simplified formula to estimate the number of years required to double the investment at a fixed annual rate of interest, you divide 72 by the interest rate. However, since we're looking to quadruple, not double, we need to adjust our calculation. Doubling twice equals quadrupling, so we calculate the doubling time and then multiply by 2. At a 3% interest rate, it takes 72 / 3 = 24 years to double. To quadruple, we need to double the money twice, so 24 * 2 = 48 years. The closest answer provided is 47 years, acknowledging some approximation in the rule of 72 and rounding.

Question 13

An account was opened with an investment of $1,000 ten years ago. The ending balance in the account is $1,500. If interest was compounded annually, what rate was earned on the account?

Accepted Answer

The answer of An account was opened with an investment...

Question 14

You need $2,000 to buy a new stereo for your car. If you have $800 to invest at 5% compounded annually, how long will you have to wait to buy the stereo?

Accepted Answer

The answer of You need $2,000 to buy a new...

Question 15

Six years ago, Marti invested $3,500 in an account. No other investments or withdrawals have been made. Today the account is worth $7,403.16. What rate of return has Marti earned thus far?

Accepted Answer

To find the rate of return, we can use the formula:
Final Value = Initial Value × (1 + Rate)^(Time)
where Final Value is $7,403.16, Initial Value is $3,500, and Time is 6 years.

Solving for Rate:
Rate = (Final Value/Initial Value)^(1/Time) - 1
Rate = ($7,403.16/$3,500)^(1/6) - 1
Rate = 0.133 or 13.3%

Therefore, Marti earned a rate of return of 13.3% thus far. Choice B is the best choice.

Question 16

Sue invested $5,000 eleven years ago at 12%. Terri has the same amount saved today as Sue has. Terri also earns 12% but she only invested $2,500. How long ago did Terri invest her money?

Accepted Answer

The answer of Sue invested $5,000 eleven years ago at...

Question 17

Which one of the following interest rates will produce the largest value at the end of ten years given a lump sum investment of $5,000?

Accepted Answer

Compounding more frequently (semi-annually in this case) at the same interest rate results in a higher effective interest rate due to the effect of compound interest. Therefore, among the options given, 6.0% compounded semi-annually will produce the largest value at the end of ten years.

Question 18

If the town's population was 62,000 at the end of year 5, and the population grew at the same annual rate as the number of eating establishments between the end of year 1 and the end of year
5, what was the town's population at the end of year 1 if the annual growth rate is 5.626%?

Accepted Answer

The population at the end of year 1 can be calculated using the formula for compound interest, P = A / (1 + r)^n, where P is the principal amount (population at the end of year 1), A is the amount after n years (population at the end of year 5), r is the annual growth rate, and n is the number of years. Here, A = 62,000, r = 5.626% or 0.05626, and n = 4 (from the end of year 1 to the end of year 5). Plugging these values into the formula gives P = 62,000 / (1 + 0.05626)^4, which calculates to approximately 49,809.

Question 19

One year ago, you invested $5,000. Today, your investment is worth $6,178.40. What rate of interest did you earn?

Accepted Answer

The answer of One year ago, you invested $5,000. Today,...

Question 20

The price of gold has gone from $250 an ounce to approximately $1,600. Given an annual growth rate of 8.04%, how long did it take gold to reach its highest value?

Accepted Answer

The answer of The price of gold has gone from...

Quiz 5: Introduction to Valuation: the Time Value of Money