Affordable Mortgage, Loans, and Purchase Price
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Kim and Dan Bergholt are both government workers. They are considering purchasing a home in the Washington D.C. area for about $280,000. They estimate monthly expenses for utilities at $220, maintenance at $100, property taxes at $380, and home insurance payments at $50. Their only debt consists of car loans requiring a monthly payment of $350.
Kim's gross income is $55,000 per year and Dan's is $38,000 per year. They have saved about $60,000 in a money market fund on which they earned $5,840 last year. They plan to use most of this for a 20% down payment and closing costs. A lender is offering 30-year variable rate loans with an initial interest rate of 8% given a 20% down payment and closing costs equal to $1,000 plus 3 points.
Before making a purchase offer and applying for this loan, they would like to have some idea whether they might qualify.
Estimate the affordable mortgage and the affordable purchase price for the Bergholts.
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Solution Summary
This response calculates whether a couple is able to apply for a loan, depending on the estimated affordable mortgage and purchase price of the house they wish to buy.
Solution Preview
To judge their qualification for the 30 year variable rate loan, we need to estimate weather the Bergholts can afford the loan or not. We need to compute all the annual costs relating to the loan plus other expenses. We then compare costs to the combined annual income. If costs are greater than income, they cannot afford the loan and would not be qualified, and vice versa.
Annual repayment cost of mortgage is
Final value of mortgage = price * (1 - down payments) (1+r) ^ n
= 280,000 (1-20%) * (1.08) ^ 30 = 2,254,035
Sum of repayments can be formulated by
S = {[A* (1+r) ^ (n -1)] / r} = [A* 1.08^(30 - 1)] / 0.08 ...
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