Question

1. A house pays its owner $3000/month if the owner rents it out. Assume the house exists forever. You are considering buying a house or renting. The annual interest rate is 5%. If the house sells for $500,000, should you buy or rent? Assume you have the cash and you don't need to take a mortgage.

Answer 1

Annual interest rate = 5%

Let the effective monthly interest rate be r%

(1+r%)^12 = (1+5%)^1

=> (1+r%) = 1.05^(1/12)

=> r% = 1.05^(1/12) - 1

=> r% = 0.4074%

Monthly rent = $3,000

Duration = ∞

(P/A, i, ∞) = 1/i

PW of renting = -$3,000(P/A, 0.4074%, ∞) = -$3,000*(1/0.4074%) = -$3,000*(1/{0.4074/100}) = -$736,377

PW of buying = -$500,000

As the present worth of buying the house is greater than that of renting the house(note that the negative sign is included in the comparison), you should buy the house.