Question

You are interested in buying a house and renting it out. You expect to receive a monthly net income of $1450 from rent. You then expect to sell the house for $329,000 at the end of 54 months. If your discount rate on this investment is 9% per year (compounded monthly), how much is this property worth to you today? Assume that you receive rent at the beginning of each month and you receive the first rent the same day you purchase the property. Round to the nearest cent. ​[Hint: 1) This is a monthly annuity due combined with a single cash flow at the end, and you are looking for the total PV. 2) The question provides the number of months, not years; so nxm is directly given to you. 3) The discount rate provided is compounded monthly, so you need to discount both the annuity due and the single cash flow at the end using the PV formulas with monthly compounding.]

Answer 1

Monthly rent as annuity due =1450
Rate per month =9%/12 =0.75%
House value at the end of 54 months =329000
The Value of property worth to you =PV of rent using annuity due formula+PV of Future Value of House
=(1+r)*((1-(1+r)^-n)/r)+Fv/(1+r)^n =(1+0.75%)*1450*((1-(1+0.75%)^-54)/0.75%)+329000/(1+0.75%)^54 =284438.12