Question 1

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%?
A) 49,809
B) 51,435
C) 53,230
D) 54,330
E) 56,730

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 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.
A) 4.2%
B) 4.7%
C) 5.6%
D) 8.3%
E) 9.3%

Accepted Answer

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

Question 3

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?
A) 3.43%
B) 3.45%
C) 3.48%
D) 3.52%
E) 3.55%

Accepted Answer

The interest rate can be found using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values ($A = 306,958$, $P = 250,000$, $n = 6$) into the formula gives $r = \left(\frac{306,958}{250,000}\right)^{\frac{1}{6}} - 1 \approx 0.0348$ or 3.48%.

Question 4

At a 6% rate of interest you will double your money in approximately ___ years.
A) 3
B) 6
C) 12
D) 24
E) 48

Accepted Answer

The rule of 72 is a simple way to estimate the number of years required to double the investment at a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself. In this case, 72 divided by 6 equals 12 years.

Question 5

One year ago, you invested $5,000. Today, your investment is worth $6,178.40. What rate of interest did you earn?
A) 16.23%
B) 16.45%
C) 22.18%
D) 23.57%
E) 24.09%

Accepted Answer

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

Question 6

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?
A) 12.86%
B) 13.30%
C) 15.96%
D) 18.58%
E) 19.20%

Accepted Answer

The answer of Six years ago, Marti invested $3,500 in...

Question 7

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?
A) 6.58 years
B) 8.42 years
C) 14.58 years
D) 15.75 years
E) 18.78 years

Accepted Answer

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

Question 8

All County Insurance, Inc. promises to pay Ted $1 million on his 65^thbirthday in return for a one-time payment of $75,000 today. (Ted just turned 25) At what rate of interest would Ted be indifferent between accepting the company's offer and investing the premium on his own? A) 2.4% B) 5.5% C) 6.1% D) 6.7% E) 7.2%

Accepted Answer

The interest rate that makes Ted indifferent is the rate at which the present value of $1 million received at age 65 equals the $75,000 invested today. Using the formula for future value, the rate is approximately 6.7%.

Question 9

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?
A) 16 years
B) 17 years
C) 18 years
D) 19 years
E) 20 years

Accepted Answer

The answer of Granny puts $35,000 into a bank account...

Question 10

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?
A) 27 years
B) 26 years
C) 25 years
D) 24 years
E) 23 years

Accepted Answer

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

Question 11

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?
A) 5.5%, compounded annually
B) 5.5%, simple interest
C) 6.0%, simple interest
D) 6.0%, compounded annually
E) 6.0%, compounded semi-annually

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 12

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?
A) 17.1 years
B) 17.4 years
C) 17.9 years
D) 21.5 years
E) 22.0 years

Accepted Answer

Terri's investment doubles in 6 years, so she has $5,000 after 12 years.

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?
A) 1.0%
B) 2.2%
C) 2.9%
D) 3.8%
E) 4.1%

Accepted Answer

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

Question 14

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.
A) 4.2%
B) 4.7%
C) 5.6%
D) 8.7%
E) 9.3%

Accepted Answer

The growth rate can be calculated using the formula for compound annual growth rate (CAGR), which is $CAGR = \left( \frac{V_f}{V_i} \right)^{\frac{1}{n}} - 1$, where $V_f$ is the final value, $V_i$ is the initial value, and $n$ is the number of periods. Here, $V_f = 138$, $V_i = 115$, and $n = 4$ years (from the end of year 1 to the end of year 5). Plugging these values into the formula gives a CAGR of approximately 4.7%.

Question 15

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?
A) 2.69 years
B) 3.33 years
C) 5.17 years
D) 6.67 years
E) 10.31 years

Accepted Answer

To find out how much sooner Sampson could have sold the company for $3 million instead of $3,713,459, we first calculate the number of years it took to reach both amounts using the formula for compound interest: A = P(1 + r)^t, where A is the amount, P is the principal, r is the rate, and t is the time in years.For $3,713,459:3,713,459 = 1,325,000(1 + 0.0825)^tSolving for t gives approximately 16.67 years.For $3,000,000:3,000,000 = 1,325,000(1 + 0.0825)^tSolving for t gives approximately 14 years.Subtracting the two times: 16.67 years - 14 years = 2.67 years.

Question 16

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?
A) 13 years
B) 14 years
C) 15 years
D) 16 years
E) 17 years

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 17

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.
A) 11.5%
B) 12.8%
C) 14.6%
D) 15.6%
E) 23.1%

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 approximately 11.5%.

Question 18

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.
A) 2.5 years
B) 2.8 years
C) 3.0 years
D) 3.2 years
E) 3.5 years

Accepted Answer

Moe's investment grew at 9% annually to double in value, which can be calculated using the formula for compound interest: $A = P(1 + r)^t$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. For Moe, solving $1992.56 = 1000(1 + 0.09)^t$ gives $t$ close to 8 years. For Joe, using the same formula with his interest rate, $1992.97 = 1000(1 + 0.0647)^t$, gives $t$ close to 11 years. The difference in time, therefore, is about 3 years, indicating Joe invested his money 3 years before Moe.

Question 19

At a 3% rate of interest, you will quadruple your money in approximately ____ years.
A) 3
B) 6
C) 12
D) 24
E) 47

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 20

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.
A) 172
B) 198
C) 202
D) 223
E) 225

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, giving an average annual growth rate of 5.75 restaurants per year. Applying this growth rate for the next 5 years (5.75 * 5 = 28.75), the forecasted number of restaurants at the end of year 10 is approximately 138 + 28.75 = 166.75, which rounds to 172.

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

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%?

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?

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

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

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?

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?

All County Insurance, Inc. promises to pay Ted $1 million on his 65thbirthday in return for a one-time payment of $75,000 today. (Ted just turned 25) At what rate of interest would Ted be indifferent between accepting the company's offer and investing the premium on his own?

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?

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?

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?

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?

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?

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?

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?

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.

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.

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

All County Insurance, Inc. promises to pay Ted $1 million on his 65^thbirthday in return for a one-time payment of $75,000 today. (Ted just turned 25) At what rate of interest would Ted be indifferent between accepting the company's offer and investing the premium on his own?