You purchase a $325,000 town home and you pay 25 percent down. You obtain a 30-year fixed-rate mortgage with an annual interest rate of 5.75 percent. After five years you refinance the mortgage for 25 years at a 5.1 percent annual interest rate. After you refinance, what is the new monthly payment (to the nearest dollar)

Answer:New Monthly Payments = $1613.81

Explanation:

Present Value = $ 325000 (1 - 0.25) = 243750

n = 30 x 12 = 360

R = 5.75%/12

Monthly payments (30 year Bond) = rPV / (1 - (1+R) ^-n)

Monthly payments (30 year Bond) = (0.0575/12 x 243750) / (1 - (0.0575/12^-30))

Monthly payments (30 year Bond) = 1167.9687338 / 0.1335983624

Monthly payments (30 year Bond) = 8742.38810013 = 8742.39

Balance of the loan in 5 years

Balance = PV (1+r) ^n - P ((1+r) ^n - 1) / r

Balance = 243750 (1 + 0.0575) ^5 - 8742.39 ((1 + 0.0575) ^5 - 1) / 0.0575

Balance = 322363.9769 - 49036.27513 = 273327.70177

Balance = 273327.70

New Monthly Payments = (0.0510/12 X 273327.70) / (1 - (1 + 0.510/12) ^-300)

New Monthly Payments = 1161.642725 / 0.7198130660

New Monthly Payments = 1613.811684 = $1613.81