Question

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 percent annual rate or a 15 year mortgage at 4 percent. 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? Must show work.

Answer 1

PV of loan Amount = Loan amount - Down Payment = 500,000 - 100,000 = 400,000
Considering 30 year Mortgage  
Rate Per Month = 4.5%/12 = 0.375%
Number of Periods = 12*30 = 360
Monthly Payments = PV/(1-(1+r)^-n)/r = 400,000/(1-(1+0.375%)^-360)/0.375% = 2,026.74
Monthly Payments with insurance and taxes = 2026.74 + 1000 = 3026.74

Considering 15 year Mortgage  
Rate Per Month = 4%/12 = 0.375%
Number of Periods = 12*15 = 180
Monthly Payments = PV/(1-(1+r)^-n)/r = 400,000/(1-(1+4%/12)^-180)/4%/12 = 2,958.75
Monthly Payments with insurance and taxes = 2,958.75 + 1000 = 3958.75

Kathy and Stan can choose for long term loan if they expect inflation to be high (30 year mortgage plan)

However if inflation is low then taking up short term loan is better(15 year mortgage plan)

Please Discuss in case of Doubt

Best of Luck. God Bless
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