a first - time home buyer is given the choice of two loans:\nloan a\n$390,000\n15 year - fixed\n4 discount…

a first - time home buyer is given the choice of two loans:\nloan a\n$390,000\n15 year - fixed\n4 discount points\nm = $3,509.71\nloan b\n$390,000\n15 year - fixed\n0 discount points\nm = $3,659.86\nhow much does the home buyer save in total by choosing loan a?\n$27,027.00\n$11,427.00\n$26,351.02\n$42,627.05

a first - time home buyer is given the choice of two loans:\nloan a\n$390,000\n15 year - fixed\n4 discount points\nm = $3,509.71\nloan b\n$390,000\n15 year - fixed\n0 discount points\nm = $3,659.86\nhow much does the home buyer save in total by choosing loan a?\n$27,027.00\n$11,427.00\n$26,351.02\n$42,627.05

Answer

Explanation:

Step1: Calculate total payment for Loan B

The loan term is 15 years. There are (12) months in a year, so the total number of months (n = 15\times12=180). The monthly payment for Loan B is (M_B=$3659.86). The total payment for Loan B is (T_B = M_B\times n). [T_B=3659.86\times180=$658774.8]

Step2: Calculate total payment for Loan A

The monthly payment for Loan A is (M_A = $3509.71). The total payment for Loan A (excluding discount - points) is (T_A'=M_A\times n). [T_A'=3509.71\times180=$631747.8] One discount - point is (1%) of the loan amount. The loan amount (L=$390000). For 4 discount - points, the cost of discount - points (C = 4%) of (L), so (C=0.04\times390000=$15600) The total payment for Loan A (including discount - points) is (T_A=T_A'+C). [T_A = 631747.8+15600=$647347.8]

Step3: Calculate the savings

The savings (S=T_B - T_A). [S=658774.8-647347.8=$11427]

Answer:

($11,427.00)