Question 1

Calculate the effective annual rate for 14.4% compounded monthly.
A) 15.4%
B) 12.8%
C) 16.4%
D) 13.8%
E) 17.1%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: EAR = (1 + i/n)^(n*1) - 1, where i is the annual interest rate and n is the number of compounding periods per year. For 14.4% compounded monthly, i = 0.144 and n = 12. Plugging these values into the formula gives EAR = (1 + 0.144/12)^(12*1) - 1 = 1.154967 - 1 = 0.154967, or 15.4%.

Question 2

Calculate the effective annual rate for 9.4% compounded quarterly.
A) 13.14%
B) 12.88%
C) 10.58%
D) 9.74%
E) 9.98%

Accepted Answer

The answer of Calculate the effective annual rate for 9.4%...

Question 3

Calculate the effective annual rate for 19.2% compounded semi-annually.
A) 21.72%
B) 20.12%
C) 23.44%
D) 22.72%
E) 19.94%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: $(1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate (expressed as a decimal) and $n$ is the number of compounding periods per year. For 19.2% compounded semi-annually, $r = 0.192$ and $n = 2$. Plugging these values into the formula gives: $(1 + \frac{0.192}{2})^2 - 1 = (1 + 0.096)^2 - 1 = 1.20192 - 1 = 0.20192$, or 20.12%.

Question 4

Calculate the effective annual rate for 18% compounded annually.
A) 19.8%
B) 16.8%
C) 18.0%
D) 19.0%
E) 20.6%

Accepted Answer

The effective annual rate (EAR) for an interest rate compounded annually is simply the nominal rate itself, which in this case is 18%.

Question 5

Many department stores charge 2.4% per month on overdue accounts. What is the effective annual rate in this situation?
A) 26.8%
B) 32.9%
C) 25.6%
D) 31.8%
E) 28.8%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: EAR = (1 + i/n)^(n*t) - 1, where i is the nominal rate, n is the number of compounding periods per year, and t is the number of years. Here, i = 2.4% per month = 0.024, n = 12, and t = 1. So, EAR = (1 + 0.024)^12 - 1 = 0.329 or 32.9%.

Question 6

What monthly compounded nominal rate has an effective rate of 14.29%
A) 11.93%
B) 13.43%
C) 15.26%
D) 13.92%
E) 13.20%

Accepted Answer

The answer of What monthly compounded nominal rate has an...

Question 7

Calculate the effective annual rate if $100 grew to $165 in 11.5 years with quarterly compounding.
A) 10.94%
B) 4.38%
C) 7.87%
D) 7.22%
E) 4.45%

Accepted Answer

The answer of Calculate the effective annual rate if $100...

Question 8

On overdue accounts the telephone company charges 1.25% per month. What is the effective annual rate?
A) 17.92%
B) 17.55%
C) 16.33%
D) 16.08%
E) 15.00%

Accepted Answer

The answer of On overdue accounts the telephone company charges...

Question 9

Over six years Craig earned interest of $8,400 on an investment of $20,000. What effective rate of return did he earn?
A) 15.56%
B) 6.02%
C) 7.00%
D) 11.53%
E) 14.71%

Accepted Answer

The effective rate of return can be calculated by dividing the total interest earned by the total amount invested and then dividing by the number of years. So, $8,400 / $20,000 = 0.42 over 6 years gives an annual rate of 0.42 / 6 = 0.07 or 7%. However, since the question asks for the effective rate of return, we need to consider the annual rate in terms of percentage, which is 7%. The mistake in the calculation was not converting the annual rate correctly to a percentage. The correct calculation should involve finding the rate that matches the given interest over the investment period, which requires a more detailed analysis considering the compound interest formula or an approximation method if the interest is compounded annually. Given the options and the total interest earned over the period, the correct effective rate of return is closer to 6.02% when considering the time value of money and the effect of compounding, if any, over the six years.

Question 10

Over nine years Craig earned interest of $29,700 on an investment of $16,000. What effective rate of return did he earn?
A) 7.11%
B) 9.44%
C) 10.92%
D) 12.37%
E) 13.56%

Accepted Answer

The answer of Over nine years Craig earned interest of...

Question 11

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 when given 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, we solve for $r_{M}$ to find the equivalent monthly rate. The calculation shows that the monthly rate that equates to a 7.8% semi-annual rate is approximately 7.68% when compounded monthly.

Question 12

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 find the semi-annually compounded nominal rate equivalent to a 10.5% rate compounded monthly, we use the formula for converting interest rates: $ (1 + \frac{r_m}{m})^m = (1 + \frac{r_s}{s})^s $, where $r_m$ is the monthly rate, $m$ is the number of times the interest is compounded per year for the monthly rate, $r_s$ is the semi-annual rate, and $s$ is the number of times the interest is compounded per year for the semi-annual rate. Given a 10.5% annual rate compounded monthly, $r_m = 0.105$ and $m = 12$. We are looking for $r_s$ with $s = 2$. Rearranging the formula and solving for $r_s$, we find that the equivalent semi-annually compounded nominal rate is approximately 10.73%.

Question 13

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 14

A mutual fund paid 3.5%, 4%, 3.5%, 6% and 5% over the past five years. If you had invested $1000 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) $1227.98
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 investment. Starting with $1000:1st year: $1000 * (1 + 3.5%) = $1000 * 1.035 = $10352nd year: $1035 * (1 + 4%) = $1035 * 1.04 = $1076.403rd year: $1076.40 * (1 + 3.5%) = $1076.40 * 1.035 = $1114.074th year: $1114.07 * (1 + 6%) = $1114.07 * 1.06 = $1180.915th year: $1180.91 * (1 + 5%) = $1180.91 * 1.05 = $1240.96It appears there was a calculation error in the provided options and explanation. Correcting the calculation for the 5th year:5th year: $1180.91 * (1 + 5%) = $1180.91 * 1.05 = $1240.96None of the provided options exactly match the corrected calculation, indicating a mistake in the initial calculation or in the provided options. The correct calculation method is shown, but the final answer does not match due to a likely mistake in the calculation or in the provided options.

Question 15

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 16

Calculate nominal rate of interest (to the nearest 0.01%):

Accepted Answer