Answer:
a. The amount you could afford to pay now for this property is $134,765.04.
b. Effective annual rate (EAR) = 5.12%
Explanation:
a. If i 8.6% per year (the MARR) is an acceptable interest rate, how much could you afford to pay now for this property if it is estimated to have a resale value of $150,000 9 years from now?
Step 1: Calculation of the present value of the annual net cash inflow
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PVAC = AC * ((1 - (1 / (1 + i))^n) / i) …………………………………. (1)
Where;
PVAC = Present value of the annual cash inflow = ?
AC = Annual net cash inflow = (Annual rent * Number of months in a year) – Annual property upkeep expense – Annual property tax = ($1,200 * 12) - $3,000 - $1,000 = $10,400
i = annual interest rate = 8.6%, or 0.086
n = number of years = 9
Substitute the values into equation (1), we have:
PVAC = $10,400 * ((1 - (1 / (1 + 0.086))^9) / 0.086) = $63,377.43
Step 2: Calculation of the present value of the resale value
This can be calculated using the formula for calculating the present value as follows:
PVRV = RV / (1 + i)^n ........................... (2)
Where;
PVRV = present value of the resale value = ?
RV = resale value = $150,000
i = annual interest rate = 8.6%, or 0.086
n = number of years = 9
Substitute the values into equation (2), we have:
PVRV = $150,000 / (1 + 0.086)^9 = $71,387.61
Step 2: Calculation of the amount you could afford to pay now for this property
PVAC = Present value of the annual cash inflow = $63,377.43
PVRV = present value of the resale value = $71,387.61
Amount you could afford to pay now = PVAC + PVRV = $63,377.43 + $71,387.61 = $134,765.04
b. Let's assume that the interest rate is 5%. If the 5% interest had been a nominal interest rate, what would the corresponding effective annual interest rate have been with bi-weekly (every two weeks) compounding?
The effective annual rate (EAR) can be calculated using the following formula:
EAR = ((1 + (i / n))^n) - 1 .............................(3)
Where;
i = Annual nominal interest rate = 5%, or 0.05
n = Number of compounding periods in a year = Number of bi-week in a year = Number of weeks in a year / 2 = 52 / 2 = 26
Substitute the values into equation (3), we have:
EAR = ((1 + (0.05 / 26))^26) - 1 = 0.0512206204121786, or 5.12206204121786%
Rounding to 2 decimal places, we have:
EAR = 5.12%
