The remaining Application Exercises deal with purchasing a house. Assume that you are currently renting an apartment for $1,040 per month and you have been considering buying a house. You have saved $10,000 towards a down payment for the house. A salesperson informs you that he has a new house for sale, where the house and land were independently appraised at $200,000, but are being sold by the builderatadiscountpriceof $185,000.Thebuilderwantstogetridofthepropertyquicklybecausethehouseisthelastonetobesoldinthedevelopmentand the builder is moving on to construction of a new development. The salesperson connects you with his in-house lender, to whom you give details about your income and grant permission to review your credit and eligibility for a loan. You inform her that you are prepared to make a down payment of $10,000 towards the house if necessary. She gets back to you with good news that, if you put $8,100 towards the house, then they can give you a 30-year loan for the balance of $176,900 at 6.25% per annum (compounded monthly). Note that lenders require the house to appraise at or above the purchase price; otherwise, they may reject the loan or require more down payment. The lender computes the monthly mortgage payment at $1,089.20. She informs you that the remaining $1,900 of your $10,000 can be used towards costs associated with the nal evaluation of the physical property and the closing of the purchase (property inspector fee, termite inspector fee, ofcial survey, attorney fees, etc.) The builder agrees to pay for costs beyond your $1,900 and make necessary repairs you identify during the period you have to inspect the property (the due diligence period). Hearing the news about your qualication for the loan, the salesperson asks you how much rent you are now paying. When you inform him that you pay $1,040 per month, he quickly points out that it would be a mere extra $50 per month for you to meet the mortgage payments. He emphasizes that it is better to own than to rent,especially if the mortage is just a bit more than your current rent. You are thrilled! After the excitement subsides, however, you decide to run the numbers yourself to make sure you get a clear understanding of what you are getting into nancially.19 The problems in this project help guide you through some of this analysis.

a) compute the numbered payment at which the unpaid balance on the loan will first dip below 80% of the original value of the house. Roughly how many years and months does it take to reach that balance?

b) Estimate the number of years and months it would take to pay off the mortgage if you double your monthly payments.