You purchase a new house for $200,000 with a 5% down payment. You obtain a 30-ye

Question

You purchase a new house for $200,000 with a 5% down payment. You obtain a 30-year loan at 5% compounded monthly and will make monthly payments on the loan. Closing costs are $1,500. PMI is $150 per month for the first 5 years. Taxes are estimated to be $1,800 per year. Insurance will be $1,500 per year.

Now, after 5 years, you have the option to refinance to a new interest rate of 4% compounded monthly. You plan to sell the house in 5 years (10 years after you bought it.) What is the most you would be willing to pay now to obtain the new interest rate of 4%? Assume your monthly MARR is 10%/12 = .8333%

Explanation / Answer

Answer: Value of new house = $200,000 Down payment = 5% of $200,000= $    10,000.00 Therefore, Value of Loan = $190,000 Term of loan = 30 years Interest rate on loan = 5% per month so, EMI on loan = $9,500.00 per month Now if he closesthe loan then closing charges = $1,500 Taxes per year = $1,800 Insurance per year = $1,500 PMI = $150 per year for 5 Years MARR per month = 0.83% Total money paid till 5 years = Future value of EMI at the end of 5 years + future value of Taxes + FV of insurance + FV of PMI at MARR Total money paid till 5 years = $753,114.23 Now the rate of interest will change to 4% therefore the selling price of the house will be the furure value of $753,114.23 after 5 years at 4% per month. Required value of the house = $7,922,481.07

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