A family is purchasing a \"traditional\" American home that has 2200 sf and pays

Question

A family is purchasing a "traditional" American home that has 2200 sf and pays, say, $100/sf. The family makes a 20% down-payment and takes out a 30-year fixed-rate mortgage for the current rate of 3.75% for the remaining 80%. Based on this scenario, How much did the house cost, in present value? How much is the down-payment? How much is the face value of the loan? Use an online mortgage calculator like the one on www.hometownlawrence.com to determine the monthly mortgage payment. Some of this mortgage is interest and some is principle. At the beginning of a 30-year mortgage, the split is about 65% interest and 35% principle. How much of the first payment is going towards principle, the portion that the family can "keep?" Of course that is only the mortgage payment. The family also has to pay property taxes. The real estate tax for the City of Harrisonburg is 69 cents per hundred dollars of assessed value per year. What is the annual property tax? (Most banks require this to be included in a monthly mortgage payment.) Of course mortgage payment and property tax are not the only costs that the banks require monthly. If the house burned down, the bank needs to be assured that the house will be replaced. Therefore they require homeowners insurance. In Harrisonburg, VA, this insurance is quite inexpensive compared to other areas of the country, probably because we don't have many hurricanes, floods, or tornadoes. Assume that home owners insurance costs $600/year for this house. What is the total monthly payment the family will be making? How much will the family spend per year?

Explanation / Answer

Cost of House = $100 x 2200 = $220,000 $220,000 x 20% = $44,000 Face value of loan = $220,000 - $44,000 = $176,000 Monthly mortgage payment: Pmt = Lr / (1-(1+r)-t) Where L = Loan, r = rate of interest per period, t = number of periods L = $176,000 r = 3.75%/12 = 0.3125% t = 30 Years x 12 months = 360 months ($176,000*0.3125%)/[1-(1+0.3125%)-360] = $815.08 Amount toward principal in first month: $815.08 x 35% = $285.28 69 cents per 100 dollars means .69% So the annual property tax = $220,000 x 0.69% = $1,518 Insurance cost per month = $600/12 = $50 Monthly payment with insurance cost = $815.08 + $50 = $865.08 Expense per year = ($815.08 x 12) + $1,518 + $600 = $11,899

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