Question 1

Determine the annual effective rate of a credit card offering 1.3% monthly.
A) 16.77%
B) 16.47%
C) 16.07%
D) 15.77%
E) 15.47%

Accepted Answer

The annual effective rate (AER) can be calculated using the formula for compound interest: $AER = (1 + r)^n - 1$, where $r$ is the monthly interest rate and $n$ is the number of compounding periods in a year. Given a monthly rate of 1.3%, or 0.013 in decimal form, and 12 compounding periods (months) in a year, the calculation is $AER = (1 + 0.013)^{12} - 1$. This equals approximately 0.1677 or 16.77% when converted to a percentage.

Question 2

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 3

What is the monthly compounded nominal rate that is equivalent to 19.56% compounded annually?
A) 18.00%
B) 15.00%
C) 21.41%
D) 19.06%
E) 18.32%

Accepted Answer

The answer of What is the monthly compounded nominal rate...

Question 4

What is the semi-annually compounded nominal rate that is equivalent to 10.5% compounded monthly?
A) 11.02%
B) 8.75%
C) 5.37%
D) 10.73%
E) 11.44%

Accepted Answer

To convert from monthly to semi-annually compounding, we need to use the formula:
nominal rate = (1 + effective monthly rate)^12 - 1
So, for 10.5% compounded monthly:
nominal rate = (1 + 0.105/12)^12 - 1
= 0.01102 or 1.102%
Now, to find the semi-annually compounded nominal rate:
nominal rate = (1 + effective semi-annual rate)^2 - 1
1.01102 = (1 + effective semi-annual rate)^2 - 1
(1 + effective semi-annual rate)^2 = 2.01102
1 + effective semi-annual rate = √2.01102
effective semi-annual rate = √2.01102 - 1
= 0.1073 or 10.73% (rounded to two decimal places)
Therefore, the answer is D.

Question 5

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 6

What is the semi-annually compounded nominal rate that is equivalent to 16% compounded quarterly?
A) 9.91%
B) 17.44%
C) 15.02%
D) 16.32%
E) 16.98%

Accepted Answer

The answer of What is the semi-annually compounded nominal rate...

Question 7

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 8

A credit card company wishes to reduce its effective interest rate by 4%. It currently charges a periodic rate of 1.75% per month. Determine by what amount the company should it set its new monthly periodic rate.
A) 1.17%
B) 1.27%
C) 1.37%
D) 1.47%
E) 1.57%

Accepted Answer

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Question 9

A bank pays a simple interest rate of 8% per annum on 40-day GICs. What is the annualized rate of return?
A) 8.00%
B) 8.29%
C) 8.77%
D) 9.13%
E) 8.53%

Accepted Answer

To find the annualized rate of return, we need to calculate the equivalent annual interest rate. Since the GIC is for 40 days, we need to adjust the rate to reflect the fact that there are more than 9 periods in a year. 
The formula for calculating the equivalent annual interest rate is: 
Equivalent annual interest rate = (1 + (simple interest rate/number of periods)) ^ (number of periods per year) - 1
In this case, the number of periods is 40/365 (since a year has 365 days). 
Substituting into the formula: 
Equivalent annual interest rate = (1 + (0.08/40/365)) ^ (365/40) - 1
= 0.0829 or 8.29%
Therefore, the best choice is B.

Question 10

What is the quarterly compounded nominal rate that is equivalent to 18% compounded monthly?
A) 18.53%
B) 17.84%
C) 16.89%
D) 18.64%
E) 18.27%

Accepted Answer

The answer of What is the quarterly compounded nominal rate...

Question 11

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 12

What amount compounded monthly is equivalent to 6.75% compounded semi-annually?
A) 5.66%
B) 6.16%
C) 6.36%
D) 6.66%
E) 7.06 %

Accepted Answer

The answer of What amount compounded monthly is equivalent to...

Question 13

What effective rate of interest is equivalent to a nominal rate of 19.214% compounded monthly?
A) 1.210%
B) 21.000%
C) 14.530%
D) 22.000%
E) 17.704%

Accepted Answer

The effective rate of interest can be calculated using the formula for converting a nominal rate compounded monthly to an effective annual rate: $E = (1 + \frac{r}{n})^n - 1$, where $E$ is the effective annual rate, $r$ is the nominal annual rate, and $n$ is the number of compounding periods per year. Plugging in the given nominal rate of 19.214% (or 0.19214 as a decimal) compounded monthly (n = 12), we get $E = (1 + \frac{0.19214}{12})^{12} - 1$, which approximately equals 0.21 or 21% when converted to a percentage.

Question 14

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

Question 15

What is the monthly compounded nominal rate that is equivalent to 7.8% compounded semi-annually?
A) 6.40%
B) 7.68%
C) 8.12%
D) 3.90%
E) 5.88%

Accepted Answer

To find the equivalent monthly compounded nominal rate from a semi-annual rate, we use the formula for converting interest rates: $ (1 + \frac{r_{SA}}{2})^2 = (1 + \frac{r_M}{12})^{12} $, where $r_{SA}$ is the semi-annual rate and $r_M$ is the monthly rate. Given a 7.8% semi-annual rate, or 0.078, we solve for $r_M$. Rearranging and solving gives an equivalent monthly rate of approximately 7.68%.

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 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 17

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 18

What amount compounded quarterly is equivalent to 7.2% compounded monthly?
A) 7.64%
B) 7.54%
C) 7.44%
D) 7.34%
E) 7.24%

Accepted Answer

The answer of What amount compounded quarterly is equivalent to...

Question 19

Determine the annual nominal rate of a credit card charging 2.3% effective rate based on monthly compounding.
A) 24.62%
B) 25.52%
C) 26.42%
D) 27.32%
E) 28.22%

Accepted Answer

The answer of Determine the annual nominal rate of a...

Question 20

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...

Quiz 9: Compound Interest: Further Topics and Applications

Determine the annual effective rate of a credit card offering 1.3% monthly.

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?

What is the monthly compounded nominal rate that is equivalent to 19.56% compounded annually?

What is the semi-annually compounded nominal rate that is equivalent to 10.5% compounded monthly?

What is the semi-annually compounded nominal rate that is equivalent to 16% compounded quarterly?

A credit card company wishes to reduce its effective interest rate by 4%. It currently charges a periodic rate of 1.75% per month. Determine by what amount the company should it set its new monthly periodic rate.

A bank pays a simple interest rate of 8% per annum on 40-day GICs. What is the annualized rate of return?

What is the quarterly compounded nominal rate that is equivalent to 18% compounded monthly?

What amount compounded monthly is equivalent to 6.75% compounded semi-annually?

What effective rate of interest is equivalent to a nominal rate of 19.214% compounded monthly?

What is the monthly compounded nominal rate that is equivalent to 7.8% compounded semi-annually?

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?

What amount compounded quarterly is equivalent to 7.2% compounded monthly?

Determine the annual nominal rate of a credit card charging 2.3% effective rate based on monthly compounding.