You are considering an option to purchase or rent a single residential property. You can rent it for $$2,000$ per month and the owner would be responsible for maintenance, property insurance, and property taxes. Alternatively, you can purchase this property for $$200,000$ and finance it with an $80$ percent mortgage loan at $6$ percent interest that will fully amortize over a $30-$year period. The loan can be prepaid at any time with no penalty.

You have done research in the market area and found that $(1)$ properties have historically appreciated at an annual rate of $3$ percent per year, and rents on similar properties have also increased at $3$ percent annually; $(2)$ maintenance and insurance are currently $$1,500\mathrm{.}00$ each per year and they have been increasing at a rate of $3$ percent per year; $(3)$ you are in a $26$ percent marginal tax rate and plan to occupy the property as your principal residence for at least four years; $(4)$ the capital gains exclusion would apply when you sell the property; $(5)$ selling costs would be $7$ percent in the year of sale; and $(6)$ property taxes have generally been about $2$ percent of property value each year.

Based on this information you must decide:

a$)$ In order to earn a $10\%$IRR after taxes on your equity, should you buy the property or rent it for a four$-$year period of ownership?

b$)$ What if your expected period of ownership was to change to five years. Would owning or renting be better if you wanted to earn a $10\%$IRR after taxes?

c$)$ Approximately what level of rents would make you indifferent between owning and renting

for a four$-$year period? Assume a $4\mathrm{.}5\%$ after$-$tax IRR would be the minimum you would need

to earn on capital invested in the home.