business math
posted by felix
Shantel and Kwamie are planning to buy their first home. Although they are excited about the prospect of being homeowners, they are also a little frightened. A mortgage payment for the next 30 years sounds like a huge commitment. They visited a few new developments and scanned the real estate listings of preowned homes, but they really have no idea how much a mortgage payment would be on a $150,000, $175,000, or $200,000 loan. They have come to you for advice.
Questions
1) After you explain to them that they can borrow money at different rates and for different amounts of time. Shantel and Kwamie ask you to complete a chart indicating what the monthly mortgage payment would be under some possible interest rates and borrowing periods. They also want to know what their total interest would be on each if they chose a 25year loan at 5% interest. Complete the chart.

felix
Rita just finished completing her educational requirements to become a dental hygienist. She has been offered jobs in two different cities and is trying to determine which one she should accept. Both employers offer similar benefits and working conditions, but the jobs are in two different states. Rita will move to the state in which she accepts a position.
The first position is in Pennsylvania. Rita would earn $50,000 a year, and she could purchase a starter duplex in the older part of the city for about $75,000. Property taxes equal about 3.5% of assessed value. Assessed value is normally 85% of market value. The state sales tax rate is 6% but does not apply to clothing or food among other items. State income taxes average 3%.
The other position is in Maryland. Rita would earn $65,000 a year, but a starter duplex would cost her $135,000. In that area, property taxes average about 4% of assessed value, and values are assessed at 60% of market value. The state sales tax is generally considered to be about 1% higher than in Pennsylvania because it applies to clothing as well as other purchases. Additionally, state income taxes average 1.5% higher in Maryland than in Pennsylvania.
What would be the difference in cost of living between the two locations based only on the differences in sales tax, income tax, and property tax? Assume $24,000 of taxable purchases for this exercise.
Using your answers from Question 1, what percentage of the difference in annual salaries does this additional cost represent? 
MathMate
A very nice thinking question!
To compare the two jobs, you would first need to tabulate expenditures.
House purchase and mortgages aside (important issues though), you need to list, for each city,
1. annual property tax
2. state income tax
3. assume a percentage of income spent on purchases (say 25% on food, and 50% on taxable items), calculate the sales tax.
Sum up the three, call it S.
Next, assume a 25year mortgage and 5% APR (as in Q1), calculate the annual mortgage payment, assuming a $5500 downpayment (about 10%), call it M.
Compare the sum S+M for each city, and make your comments.
This is an analysis question with some necessary assumptions. I suggest you examine the proposed steps above, critique on the assumptions, before proceeding to the calculations and conclusions.
If you have any questions, please post here (as opposed to a new thread, unless you refer to this post in the new thread).
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