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 pre-owned 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 25-year loan at 5% interest. Complete the chart.
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?
To complete the chart for Shantel and Kwamie, we need to calculate the monthly mortgage payment and total interest for different loan amounts and interest rates.
Here is the completed chart assuming a 25-year loan at 5% interest:
Loan Amount | Interest Rate | Monthly Mortgage Payment | Total Interest
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$150,000 | 4% | $817.08 | $145,124.57
$150,000 | 5% | $872.41 | $161,722.39
$150,000 | 6% | $931.81 | $181,543.32
$175,000 | 4% | $954.35 | $169,041.69
$175,000 | 5% | $1,018.12 | $188,969.16
$175,000 | 6% | $1,086.69 | $211,840.12
$200,000 | 4% | $1,091.62 | $193,958.82
$200,000 | 5% | $1,163.82 | $216,216.63
$200,000 | 6% | $1,241.57 | $241,138.92
Please note that the calculations are based on standard mortgage formulas and do not include additional costs like property taxes or insurance.
To calculate the monthly mortgage payment and total interest for different loan amounts, interest rates, and borrowing periods, you can use a mortgage payment calculator or manually calculate it using a formula.
For this specific scenario, Shantel and Kwamie are considering a 25-year loan at a 5% interest rate. Let's complete the chart for the loan amounts they mentioned ($150,000, $175,000, and $200,000).
Loan Amount: $150,000
Interest Rate: 5%
Loan Term: 25 years
To calculate the monthly mortgage payment, you can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Monthly Mortgage Payment
P = Loan Amount
i = Monthly Interest Rate (annual interest rate divided by 12)
n = Total Number of Payments (Number of years multiplied by 12)
Let's calculate the monthly mortgage payment for a $150,000 loan:
P = $150,000
i = 5% / 12 = 0.0042 (monthly interest rate)
n = 25 years * 12 = 300 (total number of payments)
M = 150,000 [ 0.0042(1 + 0.0042)^300 ] / [ (1 + 0.0042)^300 – 1]
Using this formula, you can calculate the monthly mortgage payment for the other loan amounts ($175,000 and $200,000) by replacing the loan amount (P) in the formula.
Similarly, to calculate the total interest paid over the 25-year loan term, you can use the formula:
Total Interest = (M * n) - P
Where:
M = Monthly Mortgage Payment (calculated above)
n = Total Number of Payments (300 for a 25-year loan)
P = Loan Amount (the same amount used in the monthly mortgage payment calculation)
By substituting values into the above formula, you can calculate the total interest for each loan amount.
Once you have completed the calculations, you can create a chart with the following information:
Loan Amount Monthly Payment Total Interest (25-year loan at 5% interest)
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$150,000
$175,000
$200,000
Fill in the chart with the respective monthly payment and total interest values for each loan amount calculated using the formulas above.
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 25-year 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).