Question 1

You want to take out a fully-amortizing 30-year mortgage. You can afford monthly payments of $600 each. The interest rate is 9%. How much money can you borrow?

Accepted Answer

The amount of money you can borrow with a fully amortizing loan can be calculated using the formula for the present value of an annuity: $P = \frac{PMT}{r} \left(1 - \frac{1}{(1 + r)^n}\right)$, where $P$ is the loan principal, $PMT$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. Given a monthly payment ($PMT$) of $600, an annual interest rate of 9% (which is 0.09/12 = 0.0075 monthly), and a loan term of 30 years (which is 30*12 = 360 months), the calculation is as follows: $P = \frac{600}{0.0075} \left(1 - \frac{1}{(1 + 0.0075)^{360}}\right)$, which approximately equals $74,569.

Question 2

What is the monthly payment on an $80,000, 9% interest-only mortgage?

Accepted Answer

Interest-only mortgage payments are calculated by multiplying the loan amount by the interest rate and dividing by 12 months. For an $80,000 loan at 9% interest, the monthly payment is $80,000 * 0.09 / 12 = $600.

Question 3

For the two questions below, consider the following period-by-period total returns:
Year 1: 5.00%
Year 2: 15.00%
Year 3: 25.00%
-What is the arithmetic average total return per year for the Years 1-3 period?

Accepted Answer

The arithmetic average total return per year is calculated by summing the total returns for each year and then dividing by the number of years. So, (5.00% + 15.00% + 25.00%) / 3 = 45.00% / 3 = 15.00%.

Question 4

If a property will produce net cash flow that grows at a rate of 1.5% per year in perpetuity, and the opportunity cost of capital is 12%, then what is the "cap rate" net cash flow / property value) for the property?

Accepted Answer

The cap rate is calculated as the opportunity cost of capital minus the growth rate of the net cash flow. Therefore, it is 12% - 1.5% = 10.5%.

Question 5

For the two questions below, consider the following period-by-period total returns:
Year 1: 5.00%
Year 2: 15.00%
Year 3: 25.00%
-What is the geometric average total return per year for the Years 1-3 period?

Accepted Answer

The geometric average return is calculated by finding the product of the returns (expressed as a decimal plus one), taking the nth root (where n is the number of returns), and then subtracting one and converting back to a percentage. For these returns, the calculation is: [(1.05) * (1.15) * (1.25)]^(1/3) - 1 = 0.1471 or 14.71%.

Question 6

The nominal appreciation return was:

Accepted Answer

The nominal appreciation return refers to the increase in value of an asset or investment expressed as a percentage. Given the options, the correct choice is 5%, which represents a moderate increase in value.

Question 7

You need to borrow $100,000 for a down-payment on a house, and $900.00 per month is the most you can afford. How long a loan term must you get in your mortgage, if the interest rate is 9%?

Accepted Answer

The answer of You need to borrow $100,000 for a...

Question 8

The real appreciation return was:

Accepted Answer

The real appreciation return is 0% because it indicates no change in the purchasing power of the currency after adjusting for inflation.

Question 9

All are true, except:

Accepted Answer

Risk is defined as the uncertainty regarding the actual returns that will be realized from an investment compared to the expected returns. However, the statement in option B describes risk as the possibility that the actual (ex post) return may differ from the expected (ex ante) return, which is a correct definition of risk, making it not the exception to the truth among the given options. The confusion arises from the prompt's structure, which asks for the exception to true statements. Given the correct interpretation of the task, all options A, C, and D accurately describe aspects of risk and returns in finance, making them true statements. Therefore, the initial guidance to select B as the exception was incorrect based on the misunderstanding of the task's requirements.

Question 10

Suppose an asset is worth $100,000 now and in one year it will either be worth $115,000 or $95,000 with equal chance). The expected return and risk as defined in Chapter 9) are:

Accepted Answer

The expected return is calculated as the average of the possible returns: (15% + (-5%))/2 = 5%. The risk (standard deviation) is calculated as the square root of the average of squared deviations from the expected return: sqrt(((15%-5%)^2 + (-5%-5%)^2)/2) = 10%.

Quiz 3: Central Place Theory and the System of Cities