Answer:
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.
