Question

2. 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?

Answer 1

Amount to be borrowed by Kathy and Stan under both options is $400000.
Oprion 1 - 30-year mortgage at 4.5 percent annual rate
We can use the present value of annuity to calculate the monthly payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan to be borrowed = $400000
P = monthly loan payment = ?
r = interest rate per month = 4.5%/12 = 0.00375
n = number of months payments = 30 years x 12 = 360
400000 = P x {[1 - (1+0.00375)^-360]/0.00375}
400000 = P x 197.3612
P = 2026.74
Monthly loan payment = $2026.74
Oprion 2 - 15-year mortgage at 4 percent annual rate
We can use the present value of annuity to calculate the monthly payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan to be borrowed = $400000
P = monthly loan payment = ?
r = interest rate per month = 4%/12 = 0.00333
n = number of months payments = 15 years x 12 = 180
400000 = P x {[1 - (1+0.00333)^-180]/0.00333}
400000 = P x 135.1921
P = 2958.75
Monthly loan payment = $2958.75
Kathy and Stan should choose option 1 as it has less monthly outlay.