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?               _____________%

Answer 1

	Cost of home	$300,000
	Amount of the new mortgage loan	$240,000	(300000*0.8)
	Amount of down payment required	$60,000	(300000*0.2)
	Closing cost	$7,200	(0.03*240000)
	Total cash flow at closing	$67,200	(60000+7200)
	Monthly interest=(4.5/12)%
	Number of Months	360	(30*12)
	Monthly Mortgage Payment Required	$1,216.04	(Using excel PMT function withRate=(4.5/12)%, Nper=360,PV=-240000)
	Amount of Loan received in hand considering closing cost	$232,800.00	(240000-7200)
	Monthly Percentage Rate	0.3968%	(Using excel RATE function with Nper=360,Pmt=1216.04,PV=-232800)
	Annual Percentage Rate(APR)	4.76%	(0.3968*12)
	FHA Loan
	Amount of the new mortgage loan	$285,000	(300000*0.95)
	Amount of down payment required	$15,000	(300000*0.05)
	Closing cost+1.75%	$17,100	(0.06*285000
	Total cash flow at closing	$32,100	(15000+17100)
	Closing cost	$12,113	(0.0425*285000)
	Monthly interest=(5.75/12)%
	Number of Months	360	(30*12)
	Monthly Mortgage Payment including insurance	$1,663.18	(Using excel PMT function withRate=(5.75/12)%, Nper=360,PV=-285000)
	Amount of Loan received in hand considering closing cost	$267,900	(285000-17100)
	Monthly Percentage Rate	0.5274%	(Using excel RATE function with Nper=360,Pmt=1663.18,PV=-267900)
	Annual Percentage Rate(APR)	6.33%	(0.5274*12)
	Conventional Loan Down Payment plus Closing Costs	$67,200
	(Less) FHA Loan: Down Payment plus Closing Costs	$32,100
	Additional Cash Outflow for the Conventional Loan	$35,100
	Total FHA Monthly Mortgage Payment including the FHA Insurance	$1,663.18
	(Less) Conventional Monthly Mortgage Payment	$1,216.04
	Difference in Total Monthly Mortgage Payments	$447.14
	the difference in the total Cash Outflows at Closing	$35,100
	Total FHA monthly mortgage payment plus FHA Insurance Premium	$1,663.18
	(Less) Conventional monthly mortgage payment	$1,216.04
	additional monthly costs with the FHA Home Mortgage Loan	$447.14
	the Incremental cost of borrowing the additional fund	1.57%	(6.33-4.76)