$(20$ points$)$ You just bought a rent house in Fayetteville, AR$,$ for $$100,000,$ with $$20,000$ down and the balance in the form of a $15-$year amortization mortgage at a fixed rate of $5\mathrm{.}0\%$ and monthly payments.

$2$

Your principal, interest, property tax, and insurance, plus all costs of maintaining the property, are covered by your rent.

a$)$ How much are your monthly mortgage payments?

b$)$ The University grows, and prices appreciate at the rate of $6\%$ per year. What will the value of the house be in $6$ years? What will the outstanding principal of the debt be $($assume no extra payments$)?$ What will the value of the equity be$?$

c$)$ Using CAGR, what is your rate of return on your equity? Why is it so high compared to housing market price appreciation?

d$)$ At this CAGR rate, how long will it take to double your money?

e$)$ What shape of yield curve is often $($but not always$)$ followed by an economic downturn and stock market correction$/$crash$?$