Long term planning

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 payment at $50. Their only debt consists of car loans requiring a monthly payment of $350. Kim's gross income is $55,000 year and Dan is $38,000 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 cost 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.

Suppose they do qualify; what other factors might they consider before purchasing and taking out a home mortage?

What future changes might present problems for the Bergholts?

The real estate agent tells the Bergholts that if they don't care to purchase, they might consider renting. The rental option would cost 1,400 month plus utilities estimated at $220 and renter's insurance of $25 month. The Bergholts believe that neither of them is likely to be transferred to another location within the next five year. After that, Dan perceives that he might move out of government service into the private sector. Assuming they remain in the same place for the next five years, the Bergholts would like to know if it is better to buy or rent the home. They expect that the price of housing and rents will rise at an annual rate of 3% over the next five years. They expect to earn an annual rate of 5% on the money market fund. All other prices, including utilities, maintenance, and texas are expected to increased at a 3% annual rate. After federal, state and local taxes, they get to keep only 55% of a marginal dollar of earnings.

Estimate whether it is financially more attractive for the Bergholts to rent or to purchase the home over a five year holding period. Assuming the contract interest rate of 8%, monthly interest payments over the five year period would total $87,574.

Suppose it turns out that they have to relocate after one year, which is the preferred alternative after one year? Interest payments over the first year would equal $17,852.

Please help me understand. candy : (


Rent
Rent at $1,400 per month will cost $16,800 per year.
Utilities will cost $2,640 per year
Insurance will cost $300 per year.
Therefore the rent option will cost the Bergholts $19,740 per year.
Assuming a 3% rise in rent and utilities,
Year 1 costs = $19,740
Year 2 costs = 19,440 * 103% + 25 = $20,048
Year 3 costs = 20,048 * 103% + 25 = $20,675
Year 4 costs = 20,675 * 103% + 25 = $21,320
Year 5 costs = 21,320 * 103% + 25 = $21,985
Total Cost = $103,768
Applying annuity:
S = {19,440 [1.03 ^ 5 – 1] / 0.03} = $103,209
Investment in mutual fund:
S = 65,840 (1.05) ^ 5 = $84,030
Interest earned = $18,190
For the five year period the rent option would cost (103,768 – 18,190) = $85,578
And this figure would be (85,578 *100) / (5 * 51,150) = 33.5% of Bergholts’ net income over the five year holding period

Buy
Buying would cost $87,574 in interest payment for the five year period
Against this the remaining mutual fund would receive interest:
S = 9,840 (1.05) ^ 5 = $12,558
Interest earned = $2,718
For the five year period buying the house would cost (87,574 – 2,718) / 255,750 = 33.2% of Bergholts’ net income over the five year holding period. Not only would the Bergholts aquire title to the house but they would also save more if they buy and hold for five years.
One Year and Subsequent Relocation
If the Bergholts relocate in one year then for the first year rent cost would be (19,740 – 3,292 (interest earned)) = $16,448
Compared to this figure interest cost for buying would be $17,852 less interest earned ($492) = $17,360. Add to this figure the closing costs and 3 points = $1,000 + $6,720 = $7,720. The grand total for the cost of buying and relocating in a year would be (17,360 + 7,720) = $25,080. Needless to say this figure is too high and therefore the rent option would be preferable.

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