Samuel just moved to Radford and plans to live here for 5 years. He just found a perfect house to live in with his family. The current owner is willing to sell or rent the house to Samuel. The selling price will be $280000. Samuel has 20% of the house's price for down payment and also 2% of the house's price for mortgage closing cost if he buys the house. Samuel is eligible for a 30-year 4% fixed -rate mortgage loan to finish the purchase. If Samuel owns the house, he needs to pay $4700 annually for insurance and property tax, and expects the house price to increase by 1% over the 5 years. When he sells the house, he needs to pay 6% of the selling price to the realtors. If Samuel rents the house, the annual rent will be $28000. Samuel is confident that he can have an annual after-tax investment return of 5% over the next five years. Samuel does not itemize tax deductions.

Assume that all the expenses, payments, and investment payoffs occur at the end of the year. For living in the house for 5 years, what is the difference in the present value of costs between buying and renting (please report the absolute value of the difference and keep zero decimal places)?

Hints

1. In Excel, you may need functions: PMT(rate,nper, pv, fv) and NPV(rate, CF1:CFn)

2. Renting can save the down payment which can be used for investment. However, renting is also costly and Samuel will not get any equity value of the house at the end of year 5. Buying costs more now and entails subsequent mortgage payments and other costs of ownership, but Samuel can get some equity value at the end of year 5 (which can be inferred from the loan amortization schedule).

3. Because Samuel does not itemize tax deductions, we do not need to consider tax savings from the interest portion of mortgage payments.