Question

Instructions The Bainter family is moving to a new town and needs a place to live. The Bainters are considering renting or purchasing a home and have found a suitable option for each option. The home for sale is listed at $150,000.00. They have $30,000.00 for a down payment and are qualified for a fixed rate 30 -year mortgage with an annual interest rate of 4.2%. The rental home is currently $900.00 per month, with rent expected to increase approximately $75.00 every 4 years. Calculate the monthly mortgage payment amount using the formula: M=Pr(1+r)n(1+r)n−1. For each option, calculate the total costs after 1 year, 5 years, 10 years and 15 years. Include additional costs of home ownership such as taxes and home insurance. Consider advantages and disadvantages of renting versus purchasing a home. Determine which option is better over each interval: 1 year, 5 years, 10 years and 15 years. Defend conclusions with evidence. Here is the rubric for your project Factors to Consider Each person has their own unique circumstances when choosing whether to rent or purchase a home. These are several factors to consider: Length of time: The longer a person plans on living in an area, the more they can spread out the additional costs of purchasing a home. Property value: Note the median housing price declined in the late 2000s due to a housing recession. Additional costs: When purchasing a home, closing costs, interest on a mortgage, down payment, higher insurance, and property taxes can add up quickly. Tax savings: Changes to tax laws may result in an owner not being able to deduct interest on income taxes. What is the total first-year cost when purchasing the home?

Answer 1

Answer: To calculate the monthly mortgage payment amount using the formula M=Pr(1+r)n(1+r)n−1, we first need to determine the variables:

P = purchase price - down payment = $150,000 - $30,000 = $120,000

r = annual interest rate / 12 (to get the monthly rate) = 4.2% / 12 = 0.0035

n = number of payments = 30 years x 12 months per year = 360

Now we can plug these values into the formula to calculate the monthly mortgage payment:

M = $120,000 * 0.0035 * (1+0.0035)^360 / ((1+0.0035)^360 - 1)

M = $567.79

So the monthly mortgage payment amount is $567.79.

To calculate the total costs of owning vs renting over different intervals, we need to consider additional costs such as property taxes, home insurance, maintenance, and any rental increases over time.

Assuming a property tax rate of 1.5% and home insurance cost of $1,000 per year, the total costs for owning the home after 1 year would be:

Total cost of owning = down payment + (12 x mortgage payment) + property taxes + home insurance

Total cost of owning = $30,000 + (12 x $567.79) + ($150,000 x 0.015) + $1,000

Total cost of owning = $46,873.48

The total cost of renting for 1 year would be:

Total cost of renting = 12 x monthly rent

Total cost of renting = 12 x $900

Total cost of renting = $10,800

Therefore, the total cost of owning the home is higher than renting in the first year.

For the next intervals, we need to consider the rental increase every 4 years. Assuming the rental increase of $75 every 4 years, the total cost of renting after 5 years would be:

Total cost of renting = (12 x $900) + (1 x $975) + (1 x $1,050)

Total cost of renting = $11,925

Assuming an annual home maintenance cost of 1% of the home value, the total cost of owning the home after 5 years would be:

Total cost of owning = down payment + (60 x mortgage payment) + (5 x property taxes) + (5 x home insurance) + (5 x 0.01 x $150,000)

Total cost of owning = $30,000 + (60 x $567.79) + ($150,000 x 0.015 x 5) + ($1,000 x 5) + ($1,500 x 5)

Total cost of owning = $128,667.40

Therefore, the total cost of renting is lower than owning after 5 years.

We can repeat this process for 10 and 15 years to determine which option is better over each interval. However, it is important to note that the advantages and disadvantages of renting vs owning go beyond just the financial costs, and personal circumstances and priorities should also be considered.

Explanation: