Question 1

A mutual fund paid 5.5%, 9%, -8%, 3.5%, and 5% over the past five years. If you had invested $2,000 at the beginning of the five-year period, what was your investment worth at the end of the five-year period?
A) $2300.00
B) $2699.37
C) $2570.83
D) $2608.09
E) $2299.46

Accepted Answer

The answer of A mutual fund paid 5.5%, 9%, -8%,...

Question 2

Last year, Kristina purchased a new condominium in downtown Toronto for $450,000 and used the property for rental income. During the past year, she rented the condo for $2200 per month. Property taxes were $4500 for the year, and there were no other expenses. The current appraised value of the property is the same as the purchase price. What is Kristina's rate of total return?
A) 5.9%
B) 6.3%
C) 4.75%
D) 4.9%
E) 5.5%

Accepted Answer

The answer of Last year, Kristina purchased a new condominium...

Question 3

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's total return?
A) $15,000
B) $31,000
C) $16,000
D) $21,000
E) $17,100

Accepted Answer

The answer of Patty Lo purchased a house that she...

Question 4

9.1% compounded annually is a better investment than 8.8% compounded monthly.

Accepted Answer

When comparing investments, the effective annual rate (EAR) should be considered. An 8.8% interest rate compounded monthly results in a higher EAR than a 9.1% rate compounded annually.

Question 5

The insurance premium on a building is 0.05% of the face value. The face value is 75% of the building's market value. The insurance premium is $1650. What is the face value of the policy?
A) $2,475,000
B) $33,000
C) $3,300,000
D) $4,400,000
E) $44,000

Accepted Answer

The answer of The insurance premium on a building is...

Question 6

10.20% compounded monthly is equal to 10.69% compounded annually.

Accepted Answer

The effective annual rate (EAR) for 10.20% compounded monthly is calculated as (1 + 0.1020/12)^12 - 1, which equals approximately 10.69%.

Question 7

The population of Canada grew from 24,820,000 at the start 1981 to 33,740,000 at the end of 2009. The annual rate of growth over 29 years was 1.06%

Accepted Answer

The given figures show an increase from 24,820,000 to 33,740,000 over 29 years. Using the formula for annual growth rate, $ \text{Annual Growth Rate} = \left( \frac{\text{Final Population}}{\text{Initial Population}} \right)^{\frac{1}{\text{Number of Years}}} - 1 $, substituting the given values yields an approximate annual growth rate of 1.06%, confirming the statement is true.

Question 8

A portfolio earned annual rates of 18%, 25%, -5%, -5%, and 12% in five successive years. The portfolio's equivalent annual compounded rate of return is 20%.

Accepted Answer

The equivalent annual compounded rate of return, also known as the geometric mean, is calculated by multiplying the annual rates of return (plus one), taking the nth root (where n is the number of years), and then subtracting one. The given rates do not yield a 20% compounded annual growth rate when calculated correctly.

Question 9

Last year, Kristina purchased a new condominium in downtown Toronto for $450,000 and used the property for rental income. During the past year, she rented the condo for $2200 per month. Property taxes were $4500 for the year, and there were no other expenses. The current appraised value of the property is the same as the purchase price. What is Kristina's income yield?
A) 5.9%
B) 6.3%
C) 4.9%
D) 5.25%
E) 4.75%

Accepted Answer

Kristina's annual rental income is $2200 * 12 = $26,400. After subtracting the property taxes ($4500), her net income is $26,400 - $4500 = $21,900. The income yield is calculated as (Net Income / Purchase Price) * 100 = ($21,900 / $450,000) * 100 = 4.866%, which rounds to 4.9%.

Question 10

An effective rate of 6.6% (based on quarterly compounding) has a higher nominal rate than an effective rate of 6.5% (based on monthly compounding).

Accepted Answer

The nominal rate for the 6.6% effective rate with quarterly compounding is higher because it requires a higher nominal rate to achieve the same effective rate with fewer compounding periods per year compared to monthly compounding.

Question 11

5.4% compounded monthly is a better investment than 5.18% compounded semi-annually

Accepted Answer

Compounding more frequently (monthly vs. semi-annually) at a higher interest rate (5.4% vs. 5.18%) results in a greater effective annual rate, making the investment better.

Question 12

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's rate of total return?
A) 10.3%
B) 11.8%
C) 10.9%
D) 11.6%
E) 11.0%

Accepted Answer

The correct answer is A because the total return is calculated as follows:Total return = (Rental income + Appreciation) / (Initial investment + Expenses)Rental income = $1750 x 12 = $21,000Appreciation = $315,000 - $300,000 = $15,000Expenses = $3900 + $450 + $650 = $5000Initial investment = $300,000Total return = ($21,000 + $15,000) / ($300,000 + $5000) = 10.3%

Question 13

A stock valued at $150 increased by 25% and then decreased by 25%. What was the value of the stock after the decrease?
A) $140.63
B) $150.00
C) $187.50
D) $112.50
E) $125.00

Accepted Answer

The stock first increases by 25% of $150, which is $37.50, making it $187.50. Then it decreases by 25% of $187.50, which is $46.875, resulting in a final value of $140.625, rounded to $140.63.

Question 14

A $10,000 payment on March 15^th was not paid. Instead $10,158.63 was paid earning 6.4% interest compounded monthly. The payment was made on June 13.

Accepted Answer

The payment of $10,158.63 includes the original $10,000 plus interest accrued over approximately 3 months at a 6.4% annual rate, compounded monthly, which matches the scenario described.

Question 15

The average Canadian home was $70,000 in the early 80s. In 30 years, the average increased to $390,000. The average increase is 5.89%

Accepted Answer

The average annual increase can be calculated using the formula for compound annual growth rate (CAGR): CAGR = (Ending Value/Beginning Value)^(1/Number of Years) - 1. Plugging in the values: CAGR = ($390,000/$70,000)^(1/30) - 1 ≈ 0.0589 or 5.89%.

Question 16

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's income yield?
A) 7%
B) 5.7%
C) 5.6%
D) 5.3%
E) 6.6%

Accepted Answer

The answer of Patty Lo purchased a house that she...

Question 17

For an investment to double in 5 years, the interest rate has to be 14.11% compounded quarterly.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the number of years. If we want the investment to double in 5 years, then A = 2P. Substituting this into the formula, we get 2P = P(1 + r/n)^(5n). Dividing both sides by P, we get 2 = (1 + r/n)^(5n). Taking the 5th root of both sides, we get 1.1411 = 1 + r/n. Subtracting 1 from both sides, we get 0.1411 = r/n. Multiplying both sides by n, we get 0.1411n = r. Since n = 4 (quarterly compounding), we get 0.1411 * 4 = r = 0.5644, or 14.11% compounded quarterly.

Question 18

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's capital gain yield?
A) 4.8%
B) 4.7%
C) 5.3%
D) 5.6%
E) 5%

Accepted Answer

The answer of Patty Lo purchased a house that she...

Question 19

A mutual fund paid 3.5%, 4%, 3.5%, 6%, and 5% over the past five years. If you had invested $1,000 at the beginning of the five-year period, what was your investment worth at the end of the five-year period?
A) $1220.00
B) $1617.34
C) $1771.38
D) $1239.96
E) $1180.92

Accepted Answer

To calculate the value of the investment at the end of the five-year period, we apply the given percentages year by year to the initial amount. Starting with $1,000:1st year: $1,000 * (1 + 3.5%) = $1,000 * 1.035 = $1,0352nd year: $1,035 * (1 + 4%) = $1,035 * 1.04 = $1,076.403rd year: $1,076.40 * (1 + 3.5%) = $1,076.40 * 1.035 = $1,114.074th year: $1,114.07 * (1 + 6%) = $1,114.07 * 1.06 = $1,180.915th year: $1,180.91 * (1 + 5%) = $1,180.91 * 1.05 = $1,239.96Therefore, the investment would be worth $1,239.96 at the end of the five-year period.

Question 20

A stock valued at $75 decreased by 20% and then increased by 20%. What was the value of the stock after the increase?
A) $75
B) $72
C) $60
D) $90
E) $80

Accepted Answer

The stock first decreased by 20% of $75, which is $15, making it $60. Then it increased by 20% of $60, which is $12, making the final value $72.

Quiz 9: Compound Interest: Further Topics and Applications

A mutual fund paid 5.5%, 9%, -8%, 3.5%, and 5% over the past five years. If you had invested $2,000 at the beginning of the five-year period, what was your investment worth at the end of the five-year period?

9.1% compounded annually is a better investment than 8.8% compounded monthly.

The insurance premium on a building is 0.05% of the face value. The face value is 75% of the building's market value. The insurance premium is $1650. What is the face value of the policy?

10.20% compounded monthly is equal to 10.69% compounded annually.

The population of Canada grew from 24,820,000 at the start 1981 to 33,740,000 at the end of 2009. The annual rate of growth over 29 years was 1.06%

A portfolio earned annual rates of 18%, 25%, -5%, -5%, and 12% in five successive years. The portfolio's equivalent annual compounded rate of return is 20%.

An effective rate of 6.6% (based on quarterly compounding) has a higher nominal rate than an effective rate of 6.5% (based on monthly compounding).

5.4% compounded monthly is a better investment than 5.18% compounded semi-annually

A stock valued at $150 increased by 25% and then decreased by 25%. What was the value of the stock after the decrease?

A $10,000 payment on March 15th was not paid. Instead $10,158.63 was paid earning 6.4% interest compounded monthly. The payment was made on June 13.

The average Canadian home was $70,000 in the early 80s. In 30 years, the average increased to $390,000. The average increase is 5.89%

For an investment to double in 5 years, the interest rate has to be 14.11% compounded quarterly.

A mutual fund paid 3.5%, 4%, 3.5%, 6%, and 5% over the past five years. If you had invested $1,000 at the beginning of the five-year period, what was your investment worth at the end of the five-year period?

A stock valued at $75 decreased by 20% and then increased by 20%. What was the value of the stock after the increase?

A $10,000 payment on March 15^th was not paid. Instead $10,158.63 was paid earning 6.4% interest compounded monthly. The payment was made on June 13.