Topic $13$: Renting versus Buying

$123.$ Jennifer is choosing between buying a condominium property and renting it$.$ The price for the condo is $$157,000.$ The financing terms, if the condo is purchased, are: $LTV=0\mathrm{.}9,$ loan term $=30$ years, interest rate $=5\mathrm{.}75\%,$ monthly payments. If the condo is purchased, it is subject to immediate closing costs of $$9,420.$ Further, projected property taxes are $$2,400$ per year, monthly association fee is $$160.$ If Jennifer decides to sell the purchased condo at some point of time in the future, such sale will be subject to the agent's commission of $7$ percent. If a similar condo is rented instead, the current rent is $$1,184\mathrm{.}59$ per month. If instead of buying a condo Jennifer chooses to rent, she will invest money that otherwise would have been spent on condo into stock market. Assume that stock market yields a $9$ percent annual return. Compute the profit$/$loss of buying versus renting for different periods of time spent in the purchased condo until it is sold for two different scenarios of Real Estate Finance $21$ the condo's price appreciation: a$)$ Worst case, when annual price increase is $2\mathrm{.}5$ percent; b$)$ Best case, when annual price increase is $7\mathrm{.}5$ percent.$|$