Question

6) a) A mortgage (loan for buying a house) is an ordinary annuity. With a standard 30-year fixed rate loan, the money is borrowed today and paid back monthly for 30 years in a constant amount. In Yolo County the maximum conforming loan amount is $552,000. A conforming loan meets conditions set by government sponsored entities (GSE) called Fannie Mae and Freddie Mac in the US. Conforming loans usually get a lower interest rate because the bank can sell them easily to the GSEs if they want. Suppose someone borrows $552,000 today to buy a house in Davis, CA. If the annual interest rate is 4%, with monthly compounding, what should be the fair value monthly mortgage payment? Provide a calculation. Banks will sometimes offer a homebuyer to “buy points”. This allows the homebuyer to pay money to the bank today to lower the interest rate on their mortgage. One point is 1% of the borrowed amount. For example from part a), suppose 1 point would cost $5,520 and reduce the interest rate to 3.75%. Based on the new interest rate, what would be the monthly mortgage payment? This is a tough question. Should the homebuyer take the deal from part b)? Provide a calculation. For any calculation that you do you should assume the annual interest rate is 4%. b) c)

Answer 1

	(a)
	Rate	Monthly interest rate=(4/12)%	0.3333%
	Nper	Number of months of payment	360	(30*12)
	Pv	Loan amount	$552,000
	PMT	Fair Value Monthly Mortgage Payment	$2,635.33	(Using PMT function of excel with Rate=0.3333%,Nper=360,Pv=-552000)
	(b)	Monthly payment with points
	Rate	Monthly interest rate=(3.75/12)%	0.3125%
	Nper	Number of months of payment	360	(30*12)
	Pv	Loan amount	$552,000
	PMT	Fair Value Monthly Mortgage Payment	$2,556.40	(Using PMT function of excel with Rate=0.3125%,Nper=360,Pv=-552000)
	c)
	I	Initial investment on point	$5,520
	Rate	Monthly interest rate (discount rate)	0.3333%	(4/12)%
	Nper	Number of months of payment	360
	Pmt	Monthly saving in payment	$78.93	(2635.33-2556.40)
	PV	Present Value of monthly savings	$16,533.69	(Using PV function of excel with Rate=0.3333%,Nper=360,Pmt=-78.93)
		Present Value of monthly savings is higher than initial investment on points
		Net Present Value of taking the deal	$11,013.69	(16533.69-5520)
		Net Present Value of taking the deal is positive
		Homebuyer should take the deal
										Alignment Editing Clipboard Font Number Styles Cells fe =PMT(D3,D4,-D5) D6 Н K 1 |(a) 2 Monthly interest rate=(4/12)% 0.3333% Rate Number of months of payment 360 (30*12) Nper Loan amount $552,000 Pv $2,635.33 | (Using PMT function of excel with Rate=0.3333%,Nper=360,Pv=-552000) Fair Value Monthly Mortgage Payment PMT 7 mgисне Cmpooura =PMT(D10,D11,-D12) fe D13 B K (a) 2 Monthly interest rate=(4/12)% 0.3333% Rate Number of months of payment 360 (30*12) 4 Nper $552,000 Loan amount Pv Fair Value Monthly Mortgage Payment $2,635.33 (Using PMT function of excel with Rate=0.3333%,Nper=360,Pv=-552000) PMT |(b) Monthly payment with points Monthly interest rate=(3.75/12)% Number of months of payment 0.3125% 10 Rate 360 (30*12) 11 Nper $552,000 12 Pv Loan amount $2,556.40 | (Using PMT function of excel with Rate=0.3125%,Nper=360,Pv=-552000) Fair Value Monthly Mortgage Payment 13 PMT =PV(D17,D18,-D19) D20 Н K (a) Monthly interest rate=(4/12)% Number of months of payment Rate 0.3333% 360 (30*12) 4 Nper $552,000 5 Pv Loan amount Fair Value Monthly Mortgage Payment $2,635.33 PMT (Using PMT function of excel with Rate=0.3333%,Nper=360,Pv=-552000) |(b) Monthly payment with points Monthly interest rate=(3.75/12)% Number of months of payment 0.3125% 10 Rate 360 (30*12) $552,000 11 Nper 12 Pv Loan amount Fair Value Monthly Mortgage Payment $2,556.40 (Using PMT function of excel with Rate=0.3125%,Nper=360,Pv=-552000) 13 PMT 14 c) 15 Initial investment on point $5,520 16 0.3333% (4/12)% Rate Monthly interest rate (discount rate) Number of months of payment 17 18 Nper 360 $78.93 (2635.33-2556.40) Monthly saving in payment Present Value of monthly savings 19 Pmt $16,533.69 (Using PV function of excel with Rate=0.3333%,Nper=360,Pmt=-78.93) 20 PV 21 B. 2.