A married couple are comparing the financing costs for the purchase of a $300,00
ID: 1170279 • Letter: A
Question
A married couple are comparing the financing costs for the purchase of a $300,000 home. The couple have good credit score of 790 and the required down payment, and as a result, can obtain a conventional mortgage loan with an 80 percent loan to value mortgage at a rate of 4.5% for a term of 30 year fixed rate mortgage. Closing costs for the conventional loan are 3% of the amount of the new mortgage. Compute the following for the conventional mortgage loan: Amount of the new mortgage loan__________ Amount of the Down Payment Required_________ + Total Closing Costs required at Closing ___________ = Total Cash Outflow at Closing _______________ Monthly Mortgage Payment Required______________ Annual Percentage Rate____________ Alternatively, the couple could obtain FHA mortgage financing with a 95 percent loan to value mortgage on the same property at the rate of 5.75% including the required FHA annual insurance premium for a 30 year fixed rate mortgage and 4.25% closing costs. However, with the FHA loan, an additional 1.75% is required at closing for the FHA mortgage insurance premium in addition to the 4.25% closing costs for a total cost of 6% of the new loan amount. Compute the following for the FHA mortgage loan: Amount of the new mortgage loan____________ Amount of the Down Payment Required__________ + Total Closing Costs required at Closing ___________ = Total Cash Outflow at Closing ________________ Monthly Mortgage Payment including FHA Insurance: _____________ Annual Percentage Rate_______ What are the differences in the Conventional versus the FHA mortgage Loan Cash Outflow at Closing? Conventional Loan Down Payment plus Closing Costs ____________ (Less) FHA Loan: Down Payment plus Closing Costs ____________ = Additional Cash Outflow for the Conventional Loan ____________ Total FHA Monthly Mortgage Payment including the FHA Insurance ____________ (Less) Conventional Monthly Mortgage Payment ____________ = Difference in Total Monthly Mortgage Payments ____________ What is the difference in the total Cash Outflows at Closing between the Conventional Home Mortgage Loan and the FHA Home Mortgage Loan? Conventional Home Mortgage Cash Outflow at Closing? ____________ (Less) FHA Home Mortgage Cash Outflow at Closing? ____________ Additional Cash Outflow required for the Conventional Loan ____________ Total FHA monthly mortgage payment plus FHA Insurance Premium ____________ (Less) Conventional monthly mortgage payment ____________ = Additional monthly costs with the FHA Home Mortgage Loan ____________ What is the Incremental cost of borrowing the additional funds? _____________% Show all of your work in your analysis.
Explanation / Answer
Purchase Price = $ 300000
Conventional Mortgage:
Interest Rate = 4.5%, Loan Tenure = 30 years, Loan to Value Ratio = 80 %, Closing Cost = 3 % of the Mortgage Amount.
Monthly Interest Rate = 0.375 % per month
Loan Amount = 0.8 x 300000 = $ 240000
Let the monthly repayments be $ K
Therefore, 240000 = K x (1/0.00375) x [1-{1/(1.00375)^(360)}]
K = $ 1216.045 approximately
New Mortage Loan = $ 240000, Down Payment Required = $ 60000 + 3 % of the Mortgage Amount
Cash Outflow at Closing = 0.03 x 240000 + 60000 = $ 67200
Monthly Repayments = $ 1216.045
Annual Percentage Rate = (1.00375)^(12) - 1 = 0.04594 or 4.594 %
FHA Mortgage Financing:
Interest Rate = 5.75 % per annum or 0.479167 % per month, Loan to Value Ratio = 95 %,Closing Costs = 6 % of the mortgage value, Tenure = 30 years
Loan Amount = 0.95 x 300000 = $ 285000
Let the monthly repayments be $ K
Therefore, 285000 = K x (1/0.00479167) x [1-{1/(1.00479167)^(360)}]
K = $ 1663.19
Amount of Mortgage = $ 285000
Amount of Downpayment = $ 15000
Total Closing Cost = 6 % of Mortgage Value = 0.06 x 285000 = $ 17100
Total Cash Outflow = 15000 + 17100 = $ 32100
Monthly Repayments = $ 1663.19
Annual Percentage Rate = (1.00479167)^(12) - 1 = 0.05904 or 5.904 %
Additional Cash flow for conventional mortgage = Total Cash Outflow under Conventional Mortgage - Total Cash Outflow under FHA = 67200 - 32100 = 4 35100
Difference in Monthly Mortgage Payments = Additional Monthly Cost of borrowing with the FHA Mortgage Loan = 1663.19 - 1216.045 = $ 447.145
Incremental Cost of Borrowing = APR under FHA - APR under conventional mortgage = 5.904 - 4.594 = 1.31 %
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