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)

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

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