Question 1

Calculate the EAR of 14% compounded quarterly.

Accepted Answer

The answer of Calculate the EAR of 14% compounded quarterly.
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Question 2

What is the effective annual rate of 11.25% compounded continuously?

Accepted Answer

The effective annual rate is given by the formula:$$r_{eff} = e^r - 1$$where r is the nominal annual rate.In this case, the nominal annual rate is 11.25%, so the effective annual rate is:$$r_{eff} = e^{0.1125} - 1 = 0.1191 = 11.91%$$Therefore, the correct answer is A.

Question 3

What is the annual percentage rate on a loan with a stated rate of 3% per quarter?

Accepted Answer

The annual percentage rate (APR) is calculated by compounding the quarterly rate: (1 + 0.03)^4 - 1 = 0.1255 or 12.55%.

Question 4

You borrowed $1,500 at 6% compounded annually. Your payments are $90 at the end of each year. How many years will you make payments on the loan?

Accepted Answer

The answer of You borrowed $1,500 at 6% compounded annually....

Question 5

Your local bank just loaned you $1,501. This amount is net of a 10% discount on the loan proceeds, which serves as interest on the loan. You are to repay the loan in one year. What is the effective rate at which you borrowed?

Accepted Answer

The effective rate can be calculated by dividing the interest amount by the actual loan proceeds. The interest amount is the difference between the face value of the loan and the net proceeds. If $1,501 is net of a 10% discount, the face value of the loan is $1,501 / (1 - 0.10) = $1,501 / 0.90 = $1,667.78. The interest is $1,667.78 - $1,501 = $166.78. Therefore, the effective rate is $166.78 / $1,501 = 11.11%.

Question 6

Your mother helped you start saving $10 a month beginning on your 5^thbirthday, which is on May 1^st. She always made you make your deposit on the first day of each month just to "start the month out right". Today, you turn 21 and have $6,984 in your account. What is the rate of return on your savings?

Accepted Answer

The rate of return can be calculated using the future value of an annuity formula. Given the monthly deposit, the number of deposits, and the final amount, the rate of return is approximately 13.75%.

Question 7

Calculate the EAR of 12% compounded monthly.

Accepted Answer

The answer of Calculate the EAR of 12% compounded monthly.
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Question 8

Calculate the EAR of 9% compounded quarterly.

Accepted Answer

The Effective Annual Rate (EAR) can be calculated using the formula: EAR = (1 + i/n)^(n*t) - 1, where i is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. For a 9% interest rate compounded quarterly, i = 0.09, n = 4, and t = 1. Plugging these values into the formula gives EAR = (1 + 0.09/4)^(4*1) - 1 = (1 + 0.0225)^4 - 1 ≈ 0.0931 or 9.31%.

Question 9

How many $1000 annual payments will it take to pay off a $10,000 loan if interest is 5.37% compounded annually?

Accepted Answer

The correct answer is A.The formula for the present value of an annuity is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the annuityPMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, we have:PV = $10,000PMT = $1000r = 5.37% = 0.0537n = ?Solving for n, we get:n = [1 - (1 + 0.0537)^-n] / 0.0537 * $10,000 / $1000n = 14.999Since we cannot make a fractional payment, we round up to the nearest whole number, which is 15. Therefore, it will take 15 $1000 annual payments to pay off the loan.

Question 10

Calculate the EAR of 10% compounded semi-annually.

Accepted Answer

The Effective Annual Rate (EAR) can be calculated using the formula: $EAR = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual nominal rate (in decimal form) and $n$ is the number of compounding periods per year. For a 10% rate compounded semi-annually, $r = 0.10$ and $n = 2$. Thus, $EAR = (1 + \frac{0.10}{2})^2 - 1 = (1 + 0.05)^2 - 1 = 1.1025 - 1 = 0.1025$ or 10.25%.

Question 11

At the end of each year for the next 10 years you will receive cash flows of $51. The initial investment is $321. What rate of return are you expecting from this investment?

Accepted Answer

The correct answer is A because the rate of return is 9.44%. This can be calculated using the formula: Rate of return = (Cash flows / Initial investment) * 100. In this case, the rate of return is ($51 / $321) * 100 = 9.44%.

Question 12

If you initially deposit $10,000 and contribute $1,000 per month for five years to a plan in order to accumulate $100,000, what rate of return will be required to make this happen?

Accepted Answer

The answer of If you initially deposit $10,000 and contribute...

Question 13

What is the effective annual rate of 12% compounded semi-annually?

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: $(1 + \frac{r}{n})^n - 1$, where $r$ is the nominal rate (12% or 0.12 in this case) and $n$ is the number of compounding periods per year (2 for semi-annually). Plugging in the values, we get: $(1 + \frac{0.12}{2})^2 - 1 = (1 + 0.06)^2 - 1 = 1.1236 - 1 = 0.1236$ or 12.36%.

Question 14

What is the effective annual rate of 12% compounded monthly?

Accepted Answer

The answer of What is the effective annual rate of...

Question 15

The Robertson Firm is considering a project which costs $123,900 to undertake. The project will yield cash flows of $4,894.35 monthly for 30 months. What is the rate of return on this project?

Accepted Answer

Using the financial calculator to find the IRR on this project, we can find that the rate of return is 13.59%.

Question 16

Susan has been investing $160,000 a year for the past 9 years into Sunshine in a Can, Inc. Today, as the sole shareholder, she sold Sunshine in a Can, Inc. for $2.6 million. What is her rate of return on this investment?

Accepted Answer

The answer of Susan has been investing $160,000 a year...

Question 17

A credit card company charges you an interest rate of 1.25% monthly. The annual percentage rate is ____ and the effective annual rate is _______.

Accepted Answer

The annual percentage rate (APR) is simply the monthly rate multiplied by 12, which gives 1.25% * 12 = 15.00%. The effective annual rate (EAR) takes into account the effect of compounding and is calculated as (1 + 0.0125)^12 - 1 = 0.16075 or 16.08%.

Question 18

A 13% APR compounded continuously is equal to an effective rate of:

Accepted Answer

The answer of A 13% APR compounded continuously is equal...

Question 19

Your neighbour makes you the following offer. He would like to borrow $10,000 today. He will repay the $10,000 by making yearly payments with the first payment being for $1,000 at the end of this year. The payments will grow by 10% every year thereafter. If the appropriate discount rate is 12%, how long will it take for your neighbour to repay the loan?

Accepted Answer

The correct answer is A because the present value of the payments is equal to the loan amount. The present value of the payments is calculated as follows:PV = $1,000 / (1 + 0.12)^1 + $1,100 / (1 + 0.12)^2 + $1,210 / (1 + 0.12)^3 + ...The present value of the payments is equal to $10,000, so the loan will be repaid in 12.38 years.

Question 20

What is the effective annual rate of 12% compounded continuously?

Accepted Answer

The effective annual rate is given by the formula e^r - 1, where r is the annual rate. In this case, the annual rate is 12%, so the effective annual rate is e^0.12 - 1 = 0.1275, or 12.75%.

Quiz 6: Discounted Cash Flow Valuation