Example 4 Suppose Elizabeth and Nicholas had received an estimate of their closing costs in the amount of 10,500 excluding prepaid interest and homeowners'insurance. Their lender offered them the option of reducing those costs by raising their mortgage interest rate according to the following plan: (see slides) How can they determine if it is worth taking the 4.875% APR in exchange for zero closing costs?

<br /><br />【Explanation】Determining whether it would be beneficial for Elizabeth and Nicholas to take a higher APR in exchange for zero closing costs involves estimating and comparing two costs over the lifespan of the mortgage. <br /><br />Firstly, consider keeping their initial interest rate. Their initial estimated outlay is $10,500 at closing (assuming no change in down payment affecting insurance and so on), and they continue to pay, say the original compulsory interest rate, IR1 for the mortgage.<br /><br />Least Pleasurable Alternative, LPA = Cost of Mortgage which will effectively be= $10,500 + Values predictively paid due to historial APR outstanding.<br /><br />Now, lets check the second possibility, going with a rate of $4.875\%$. This comes off as zero closing costs, hence their costs upfront is the additional values predictively present due by means of that rate over the same mortgage period<br />which we can label Convenient Caveat, CP = Increase in Mortgage due to waving off closing fees = Additional Interest due to rate hike * duration of mortgage.<br /><br />Comparing LPA and CP will help Elizabeth and Nicholas once they blacklist digit values to arrive at a greatest fit. <br /><br />If future costs(LPA) are greater than the costs of paying an increased interest rate(CP), they should opt for the higher loan. ($) Costs Initial+$ Interest Outstanding# <$ Closing Fee Waiveoff>"+4.875% of Total Outstanding Mortgage<br /><br />The difficulty lies in correctly estimating these possible two outcomes due to varying contributing factors like length of ownership plans for the property, changes in disposable incomes, financial decisions likely which add interchanging opportunity costs to both options and evaluating market conditions correctly for best decisions in response.<br /><br />【Highlight】 This is the step-by-step answer intended both for teaching the user how the problem is or may be approached logically and methodically. The 'Solution' is exempted due to it varying per individual MUDDs or alternate concepts above(as benz(MUDD)%) and made viewController(IB).\Highliight\OG. understanding contributing deductions Markup not supported.