. Kathy plans to move to Maryland and take a job at McCormick as the Assistant Director of HR. She and her husband Stan plan to buy a house in Garrison, MD and their budget is $500,000. They have $100,000 for the down payment and McCormick will pay for closing costs. They are considering either a 30 year mortgage at 4.5% annual rate or a 15 year mortgage at 4%. Calculate the monthly payment for each. Property taxes and insurance will add $1,000 per month to which ever mortgage they choose. What should Kathy and Stan do

a. For a 30-year mortgage at 4.5% annual rate, we have:

Monthly required fixed loan payment = $2,026.74

Total monthly payment = $3,026.74

Total payments for 360 months = $1,089,626.85

b. For a 15 year mortgage at 4% annual rate, we have:

Monthly required fixed loan payment = $2,958.75

Total monthly payment = $3,958.75

Total payments for 180 months = $712,575.31

c. Kathy and Stan should choose a 15 year mortgage at 4% annual.

Explanation:

a. For a 30-year mortgage at 4.5% annual rate

The monthly required fixed loan payment can be calculated using the formula for calculating loan amortization as follows:

P = (A * (r * (1 + r)^n)) / (((1+r)^n) - 1) (1)

Where:

P = Monthly required fixed loan payment = ?

A = Loan amount = House budget – Down payment = $500,000 - $100,000 = $400,000

r = monthly interest rate = 4.5% / 12 = 0.045 / 12 = 0.00375

n = number of months = 30 * 12 = 360

Substituting all the figures into equation (1), we have:

P = ($400,000 * (0.00375 * (1 + 0.00375)^360)) / (((1 + 0.00375)^360) - 1) = $2,026.74

Therefore, we have:

Monthly required fixed loan payment = $2,026.74

Total monthly payment = Monthly required fixed loan payment + Property taxes and insurance = $2,026.74 + $1,000 = $3,026.74

Total payments for 360 months = Total monthly payment * 360 = $3,026.74 * 360 = $1,089,626.85

b. For a 15 year mortgage at 4% annual rate

The monthly required fixed loan payment can be calculated using the formula for calculating loan amortization as follows:

P = (A * (r * (1 + r)^n)) / (((1+r)^n) - 1) (1)

Where:

P = Monthly required fixed loan payment = ?

A = Loan amount = House budget – Down payment = $500,000 - $100,000 = $400,000

r = monthly interest rate = 4% / 12 = 0.04 / 12 = 0.00333333333333333

n = number of months = 15 * 12 = 180

Substituting all the figures into equation (1), we have:

P = ($400,000 * (0.00333333333333333 * (1 + 0.00333333333333333)^180)) / (((1 + 0.00333333333333333)^180) - 1) = $2,958.75

Therefore, we have:

Monthly required fixed loan payment = $2,958.75

Total monthly payment = Monthly required fixed loan payment + Property taxes and insurance = $ 2,958.75 + $1,000 = $3,958.75

Total payments for 180 months = Total monthly payment * 360 = $3,958.75 * 180 = $712,575.31

c. Recommendation

Since the total payment of $712,575.31 for a 15 year mortgage at 4% annual is lower than the total payments of $1,089,626.85 for a 30-year mortgage at 4.5% annual rate, Kathy and Stan should choose a 15 year mortgage at 4% annual.

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