Assume that you are deciding to purchase a house for investment in the ideal location you prefer You would ignore all the taxes, realtor agency fees, and the transition fee in the calculation. Only consider the purchasing price as the total cost. Also, ignore the house insurance fee, etc. Only consider the purchasing price, monthly mortgage and rent.

You find and decide to buy a 3-bedroom single-family house in New Haven, CT. - The listing price is \( \$ 250,000 \). - Your downpayment is \( 20 \% \) of the price. This will be a fixed \( 80 \% \) payment mortgage loan with a \( 20 \% \) down payment. It means you will pay a \( 20 \% \) down payment at the purchase and finance \( 80 \% \) with a 30 -year mortgage. The 30-year fixed mortgage rate is \( 7.5 \% \). - You will lease the property out right after you buy it. Assume the monthly rent in the first year of your purchase is \( \$ 1500 \) /month and will stay the same for the next 30 years. The rental period is 30 years, the same as your mortgage period. In other words, you will pay off your mortgage and end the rental in 30 years. - In 30 years, you will sell the property. Assume the value of the property increases by \( 5 \% \) each year after you buy it. 1) Calculate the following value and total return. ( tips: 1) All the discount rates are the same as the mortgage rate; 2) you must show the calculation in the report to get the credit.) A. calculate the monthly mortgage payment ( 5 points) B. calculate the \( \mathbf{P V} \) of the monthly mortgage payment (5 points) C. calculate the \( \mathbf{P V} \) of the monthly rent (5 points) D. calculate the \( \mathbf{P V} \) of the resale value of the property in 30 years (5 points) 2) Then calculate the total return of your investment in the house. The discount rate is the mortgage rate. The total return on your investment property is calculated as: return \( =(\mathrm{PV} \) of cash flows subsequent to the initial investment / Initial investment \( )-1 \) (5 points \( ) \) 3) After you get the total return in 30 years, calculate the annual compound rate of return. ( 5 points) 4) Next, assume you don't purchase an investment property. Instead, you invest the same amount of your total investment in the S\&P500 index. Over the past 15 years, the S\&P 500 index is 4378.41 in 2023 and 1378.76 in 2008. Calculate the annual compound rate of return of the S\&P 500 index from 2008 to 2023. (5 points) 5) Which one could you invest in, this house or S\&P 500 index? Justify your conclusion. You need to consider the factors more than the return. (5 points)