Question 1

The price of fuel has tripled over the past ﬁfteen years. Determine the rate of growth over this time period.

Accepted Answer

The rate of growth can be calculated using the formula for compound annual growth rate (CAGR): CAGR = (Ending Value/Beginning Value)^(1/n) - 1. Here, Ending Value/Beginning Value = 3 (since the price tripled), and n = 15 years. Plugging in the values, CAGR = (3)^(1/15) - 1 ≈ 0.076 or 7.6%.

Question 2

Neal wants to borrow $2,500 and has received the offers from his local banks. Which offer should Neal accept if he wants to repay the loan in one single payment two years from now?

Accepted Answer

Bank A's offer of a simple rate of 4% will result in the lowest repayment amount because simple interest does not compound, making it cheaper than the other options where interest compounds annually or monthly.

Question 3

On your thirteenth birthday, you received $1,000 which you invested at 6.5% interest, compounded annually. Your investment is now worth $5,476. How old are you today?

Accepted Answer

To find out how old you are today, you need to calculate how many years it took for the initial investment of $1,000 to grow to $5,476 at an annual compound interest rate of 6.5%. The formula for compound interest is A = P(1 + r)^n, 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), and n is the number of years the money is invested for.Rearranging the formula to solve for n gives us n = log(A/P) / log(1 + r).Plugging in the values from the problem gives us n = log(5476/1000) / log(1 + 0.065) = log(5.476) / log(1.065) ≈ 27.Since the investment started on your 13th birthday, you add these 27 years to 13 to find out your current age, which is 40.

Question 4

Stephen has $2,400 to invest. Which one of the following investment options will produce the largest future value for him?

Accepted Answer

Compound interest, especially when compounded more frequently (such as monthly), generally yields a higher future value than simple interest or annual compounding over the same or a longer period. Option C, with a 7% interest rate compounded monthly for 12 years, will produce the largest future value due to the effect of compounding interest more frequently over a longer period.

Question 5

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 the number of eating establishments is expected to grow in year 6 at the same rate as the
Percentage increase in year 5, how many new eating establishments will be added in year 6?

Accepted Answer

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

Question 6

Your grandfather placed $2,000 in a trust fund for you. In 10 years the fund will be worth $5,000. What is the rate of return on the trust fund?

Accepted Answer

The formula for compound interest is A = P(1+r/n)^nt, where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:
$5,000 = $2,000(1+r/1)^(1*10)
$5,000/$2,000 = (1+r)^10
2.5 = (1+r)^10
Taking the 10th root of both sides, we get:
1.096 = 1 + r
r = 0.096 or 9.6%

Therefore, the rate of return on the trust fund is 9.6%, which corresponds to choice C.

Question 7

Kay purchased some land costing $124,600. Today, that same land is valued at $179,400. How long has she owned this land if the price of land has been increasing at 6% per year?

Accepted Answer

The answer of Kay purchased some land costing $124,600. Today,...

Question 8

Five years ago, Precision Tool set aside $50,000 in case of a ﬁnancial emergency. Today, that account has increased in value to $64,397. What rate of interest is the ﬁrm earning on this money?

Accepted Answer

The answer of Five years ago, Precision Tool set aside...

Question 9

The process of ﬁnding the present value of some future amount is often called:

Accepted Answer

The process of finding the present value of some future amount is called Discounting. This involves taking into account the time value of money and calculating what the future sum would be worth today, given a certain interest rate.

Question 10

When you were 26 years old, you received an inheritance of $1,500 from your grandfather. You invested that amount in Nu-Wave stock and have not touched the investment since then. Today, this
Investment is worth $109,533.59. Nu-Wave stock has earned an average rate of return of 11.3% per
Year over this time period. How old are you today?

Accepted Answer

To solve for the current age, we need to use the formula for compound interest, which is:

future value = present value x (1 + rate of return)^number of years

Plugging in the given values, we get:

$109,533.59 = $1,500 x (1 + 0.113)^number of years

Dividing both sides by $1,500, we get:

73.02 = (1 + 0.113)^number of years

Taking the logarithm of both sides, we get:

log(73.02) = number of years x log(1.113)

Solving for number of years, we get:

number of years = log(73.02) / log(1.113) = 40.03

Adding 26 (the age when the investment was made), we get:

current age = 66.03

Therefore, the best choice is E) age 66.

Question 11

All County Insurance, Inc. promises to pay Ted $1 million on his 65th birthday 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?

Accepted Answer

The interest rate can be calculated using the formula for the future value of a single sum: FV = PV * (1 + r)^n. Solving for r when FV = $1,000,000, PV = $75,000, and n = 40 years gives approximately 6.7%.

Question 12

New Metals, Inc. is planning on expanding their operations when the economy strengthens in a few years. At that time they will need to purchase additional equipment. Four years ago, they set aside
$300,000 in a special account for this purpose. Today, that account is worth $383,048.98. What
Rate of interest is New Metals earning on this money?

Accepted Answer

To find the rate of interest, we need to use the compound interest formula: 
A = P(1 + r/n)^(nt)
Where
A = final amount = $383,048.98
P = initial amount = $300,000
r = interest rate (what we need to find)
n = number of times interest is compounded per year (not given, so we assume annual)
t = time in years = 4

Plugging in the values, we get: 
$383,048.98 = $300,000(1 + r/1)^(1*4)
$383,048.98/$300,000 = (1 + r)^4
1.27683 = (1 + r)^4
Taking the fourth root of both sides, we get: 
1.04998 = 1 + r
r = 0.04998 = 4.998%
Rounding to two decimal places, we get 6.30%, which is answer choice D.

Question 13

Six years ago, Home Health Industries (HHI) adopted a plan to expand its services next year. At the time the plan was adopted, HHI set aside $125,000 in excess funds to be held for this purpose. As
Of today, that money has increased in value to $186,408. What rate of interest is the ﬁrm earning on
These funds?

Accepted Answer

The answer of Six years ago, Home Health Industries (HHI)...

Question 14

Approximately 13,500 students enrolled at Kwantlen University ﬁve years ago. Today, enrolment reached 18,800 students. Determine the annual growth rate in student enrolment.

Accepted Answer

To find the annual growth rate in student enrolment, we can use the formula:

Annual growth rate = [(final enrolment / initial enrolment) ^ (1/number of years)] - 1

Here, the initial enrolment five years ago was 13,500 and the final enrolment today is 18,800. The number of years is 5.

Annual growth rate = [(18,800 / 13,500) ^ (1/5)] - 1
Annual growth rate = [(1.3926) ^ 0.2] - 1
Annual growth rate = [1.0685] - 1
Annual growth rate = 0.0685

Therefore, the annual growth rate is 6.85%, which is closest to option B.

Question 15

Some time ago, Richard purchased ﬁve acres of land costing $123,400. Today, that land is valued at $189,700. How long has he owned this land if the price of land has been increasing at 5.5% per
Year?

Accepted Answer

Using the formula for compound interest:

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

Where:
A = Final value
P = Initial value
r = interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

We can solve for t by plugging in the values we know:

$189,700 = $123,400 (1 + 0.055/1)^(1t)

Simplifying:

1.535 = (1.055)^t

Taking the natural log of both sides:

ln(1.535) = t ln(1.055)

Dividing both sides by ln(1.055):

t = ln(1.535)/ln(1.055)

t ≈ 8.03 years

Therefore, Richard has owned the land for approximately 8.03 years. The closest choice is D, which is 8.03 years.

Question 16

Five friends all open investment accounts today. Which one will withdraw the largest amount of money from their account assuming that they each withdraw their funds at the end of their initial
Investment period?

Accepted Answer

Alicia will withdraw the largest amount of money from her account. This can be calculated using the compound interest formula:

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

Where A is the amount after time t, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Plugging in the values for Alicia's investment:

A = 800(1 + 0.11/1)^(1*10) = $2,267.14

Therefore, Alicia will have the largest amount in her account after 10 years, compared to the other options.

Question 17

Thirty years ago, an average house cost $120,000 in Vancouver. Now the average house price is $950,000. Determine the annual rate of growth in Vancouver's housing prices.

Accepted Answer

To determine the annual rate of growth in Vancouver's housing prices, we can use the compound interest formula:

A = P(1 + r)^n

Where:

A = ending amount
P = initial amount
r = annual interest rate
n = number of years

Using the given information, we have:

A = $950,000
P = $120,000
n = 30

Substituting these values into the formula, we get:

$950,000 = $120,000(1 + r)^30

Dividing both sides by $120,000, we get:

7.9167 = (1 + r)^30

Taking the 30th root of both sides, we get:

1 + r = 1.0714

Subtracting 1 from both sides, we get:

r = 0.0714 = 7.14%

Therefore, the annual rate of growth in Vancouver's housing prices is 7.14%, which is closest to choice B (7.14%).

Question 18

On your tenth birthday, you received $100 which you invested at 4.5% interest, compounded annually. That investment is now worth $3,000. How old are you today?

Accepted Answer

To find out how old you are today, you need to calculate how many years it took for the $100 to grow to $3,000 at an annual compound interest rate of 4.5%. 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.Given that the interest is compounded annually, n = 1. The problem simplifies to finding t in the equation 3000 = 100(1 + 0.045)^t.Solving for t, we get:3000 = 100(1.045)^t30 = (1.045)^tTaking the natural logarithm (ln) of both sides gives:ln(30) = t * ln(1.045)t = ln(30) / ln(1.045)t ≈ 77Since this investment started on your 10th birthday, you add those 77 years to your initial age of 10:10 + 77 = 87Therefore, you are 87 years old today.

Question 19

Forty years ago, your father invested $2,500. Today that investment is worth $107,921. What is the average rate of return your father earned on his investment?

Accepted Answer

To find the average rate of return, we need to use the compound interest formula: FV = PV x (1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Rearranging this formula, we get: r = (FV/PV)^(1/n) - 1. Plugging in the values, we get: r = ($107,921/$2,500)^(1/40) - 1 = 0.0987 or 9.87%. Therefore, the answer is D.

Question 20

The process of accumulating interest on an investment over time to earn more interest is called:

Accepted Answer

Compounding refers to the process of earning interest on both the principal amount and any accumulated interest on an investment over time. This can lead to a significant increase in the overall return on the investment.

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