Answer Each Of The Following Questions In Your Own Words

Answer Each Of The Following Questions In Your Own Words Do Not Copy

Answer Each Of The Following Questions In Your Own Words Do Not Copy

According to the problem, the McIntosh couple intends to purchase a home costing $234,900 with a 5% down payment. They are evaluating two loan options: a 15-year fixed mortgage with an APR of 2.8%, and a 30-year fixed mortgage with an APR of 3.5%. To determine the amount loaned, the down payment is subtracted from the home's price; then, monthly payments are calculated based on each loan's term and interest rate. The total amount paid over the life of each loan and the percentage of that which constitutes interest are also calculated to compare the two options.

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The first step in analyzing the McIntosh couple's mortgage options involves calculating the initial loan amount. The house price is $234,900, and with a 5% down payment, the couple deposits 0.05 times the home price, which equals $11,745. Therefore, the mortgage loan amount is the home price minus the down payment: $234,900 - $11,745 = $223,155. This is the principal amount the mortgage company will lend to the couple.

Next, for each mortgage option, the monthly payment is computed using standard amortization formulas. These formulas consider the loan amount (principal), monthly interest rate, and number of payments. The monthly interest rate is derived by dividing the annual percentage rate (APR) by 12. For the 15-year mortgage, the interest rate per month is 2.8% / 12 = 0.0023333, and the total number of payments over 15 years is 15 x 12 = 180. For the 30-year mortgage, the interest rate per month is 3.5% / 12 = 0.0029167, over 360 months.

The monthly payment (M) can be calculated using the formula:

M = P [ r(1 + r)^n ] / [ (1 + r)^n – 1 ]

where P = loan principal, r = monthly interest rate, n = number of payments.

Calculations for the 15-year mortgage:

  • P = $223,155
  • r = 0.028 / 12 = 0.0023333
  • n = 15 x 12 = 180

Applying these values yields a monthly payment of approximately $1,520.41.

Calculations for the 30-year mortgage:

  • P = $223,155
  • r = 0.035 / 12 = 0.0029167
  • n = 30 x 12 = 360

The monthly payment for the 30-year loan is approximately $1,001.41.

To determine total payments over each loan's term, multiply the monthly payment by the total number of payments: for the 15-year term, $1,520.41 x 180 = approximately $273,673.80; for the 30-year term, $1,001.41 x 360 = approximately $360,509.60.

The total interest paid is then calculated by subtracting the original loan amount ($223,155) from the total amount paid over the life of each loan. For the 15-year mortgage, interest paid will be about $273,673.80 - $223,155 = $50,518.80. For the 30-year mortgage, interest paid is about $360,509.60 - $223,155 = $137,354.60.

The percentage of total payments that is interest can be determined by dividing the total interest by the total payments and multiplying by 100%. For the 15-year loan: ($50,518.80 / $273,673.80) x 100% ≈ 18.45%. For the 30-year loan: ($137,354.60 / $360,509.60) x 100% ≈ 38.10%.

From a financial perspective, although the 15-year mortgage involves higher monthly payments, it results in significantly less total interest paid over the life of the loan. Conversely, the 30-year mortgage offers lower monthly payments but at a cost of paying substantially more interest over a longer period. I would recommend the couple opt for the 15-year fixed mortgage, as it minimizes total interest paid and helps build equity faster, despite the higher monthly payment. This choice aligns with prudent financial management, reducing long-term debt costs and increasing equity in their home (Berk, 2020). Additionally, the shorter loan term can free up income sooner for other investments or savings (Mishkin & Eakins, 2018).

References

  • Berk, J. (2020). Principles of Economics (3rd ed.). Pearson.
  • Mishkin, F. S., & Eakins, S. G. (2018). Financial Markets and Institutions (9th ed.). Pearson.
  • Investopedia. (2023). How to Calculate Mortgage Payments. https://www.investopedia.com/terms/m/mortgagepayment.asp
  • U.S. Federal Reserve. (2021). Consumer Credit and Mortgage Data. https://www.federalreserve.gov/releases/default.htm
  • Bankrate. (2023). Mortgage Rate Trends. https://www.bankrate.com/mortgages/mortgage-rates/
  • My Mortgage Insiders. (2022). Understanding Mortgage Term Options. https://www.mortgageinsiders.com/
  • CFPB. (2021). Buying a Home: How Mortgage Loans Work. https://www.consumerfinance.gov/owning-a-home/loan-options/
  • National Association of Realtors. (2022). Home Buyers and Mortgages. https://www.nar.realtor/research-and-statistics
  • Financial Samurai. (2023). The Pros and Cons of 15-Year vs. 30-Year Mortgages. https://www.financialsamurai.com/
  • Mortgage Professor. (2023). Tips for Choosing the Right Home Loan. https://mortgageprofessor.com/

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