Consdier an adjustable rate mortagage (ARM) loan for 650,000. The interest rate is indexed to the...

Consdier an adjustable rate mortagage (ARM) loan for 650,000. The interest rate is indexed to the 10-year Treasury yield. The loan has a margin 2.75%, first-year teaser rate of 2.75%, an annual rate cap of 2% and a lifetime rate cap of 5%. The loan requires monthly payments for 25 years. Assume that 10-year Treasury yields are as shown blow.

10-yr treasury yield at first anniversary date (end of year 1) 3.5%

10-yr treasury yield at the end of second year 4.25%

a) What is the debt service payment amount during the first year of the loan, and the loan balance at the end of this first year?

b) What is the contract rate on the loan for the second year?

c) What is the debt service payment during the second year and the loan balance at the end of the year?

d) What are the contract rate, monthly payment and end-of-year loan balance for year 3?

Expert Solution


	First year Teaser Rate	2.75%
	Loan Amount	$650,000
	Monthly interest	0.229167%	(2.75/12)	0.22916667
	Number of months	300	(25*12)

a)	Debt Service payment during the first year:

	Monthly amount to be paid	$ 2,998.52	(Using PMT function of excel with Rate=0.229167%,Nper=300,PV=650000)
	Debt Service payment during the first year	$ 35,982.26	(2999*12)
	MORTGAGE PAYMENT SCHEDULE DURING YEAR1

	Month	Beginning Balance	Total Payment	Interest	Principle	Ending Balance
	0					$650,000
	1	$650,000	$2,998.52	$1,489.59	$1,508.94	$648,491.06
	2	$648,491	$2,998.52	$1,486.13	$1,512.39	$646,978.67
	3	$646,979	$2,998.52	$1,482.66	$1,515.86	$645,462.81
	4	$645,463	$2,998.52	$1,479.19	$1,519.33	$643,943.47
	5	$643,943	$2,998.52	$1,475.71	$1,522.82	$642,420.66
	6	$642,421	$2,998.52	$1,472.22	$1,526.31	$640,894.35
	7	$640,894	$2,998.52	$1,468.72	$1,529.80	$639,364.55
	8	$639,365	$2,998.52	$1,465.21	$1,533.31	$637,831.24
	9	$637,831	$2,998.52	$1,461.70	$1,536.82	$636,294.42
	10	$636,294	$2,998.52	$1,458.18	$1,540.35	$634,754.07
	11	$634,754	$2,998.52	$1,454.65	$1,543.88	$633,210.20
	12	$633,210	$2,998.52	$1,451.11	$1,547.41	$631,662.78
	Loan balance at the end of first year	$631,662.78

b)	Contract Rate for secomd year
	First year teaser rate	2.75%
	Treasury yield	3.50%
	Loan margin	2.75%
	Calculated rate(3.5+2.75)=	6.25%
	Annual Rate Cap	2%
	Maximum allowed rate=	4.75%	(2.75+2)
	Contract Rate of the loan for secomd year	4.75%

c)	Loan Balance at the end of first year	$631,662.78	(Based on Mortgage schedule of year 1)
	Number of months	288	(300-12)
	Interest rate per month	0.395833333%	(4.75/12)=	0.395833333
	Monthly amount to be paid	$3,679.88	(Using PMT function of excel with Rate=0.3958333333%,Nper=288,PV=631662.78)
	Debt Service payment during second year	$44,158.54	(3679.88*12)

	MORTGAGE PAYMENT SCHEDULE DURING SECOND YEAR

	Month	Beginning Balance	Total Payment	Interest	Principle	Ending Balance
	0					$631,662.78
	1	$631,662.78	$3,679.88	$2,500.33	$1,179.55	$630,483.24
	2	$630,483.24	$3,679.88	$2,495.66	$1,184.22	$629,299.02
	3	$629,299.02	$3,679.88	$2,490.98	$1,188.90	$628,110.12
	4	$628,110.12	$3,679.88	$2,486.27	$1,193.61	$626,916.51
	5	$626,916.51	$3,679.88	$2,481.54	$1,198.33	$625,718.18
	6	$625,718.18	$3,679.88	$2,476.80	$1,203.08	$624,515.10
	7	$624,515.10	$3,679.88	$2,472.04	$1,207.84	$623,307.26
	8	$623,307.26	$3,679.88	$2,467.26	$1,212.62	$622,094.64
	9	$622,094.64	$3,679.88	$2,462.46	$1,217.42	$620,877.22
	10	$620,877.22	$3,679.88	$2,457.64	$1,222.24	$619,654.98
	11	$619,654.98	$3,679.88	$2,452.80	$1,227.08	$618,427.90
	12	$618,427.90	$3,679.88	$2,447.94	$1,231.93	$617,195.97
	Loan balance at the end of Second year	$617,195.97


d)	YEAR 3

	Treasury yield	4.25%
	Loan margin	2.75%
	Calculated rate(4.25+2.75)=	7.00%
	Annual Rate Cap	2%
	Contract Rate of the loan for secomd year	4.75%
	Maximum allowed rate in Year 3	6.75%	(4.75+2)
	Contract Rate of the loan for third year	6.75%

	Loan Balance at the end of Second year	$617,195.97	(Based on Mortgage schedule of year 2)
	Number of months	276	(288-12)
	Interest rate per month	0.5625%	(6.75/12)	0.562500000
	Monthly amount to be paid	$4,409.33	(Using PMT function of excel with Rate=0.5625%,Nper=276,PV=617195.97)
	Debt Service payment during year 3	$52,911.99	(4409.33*12)

	MORTGAGE PAYMENT SCHEDULE DURING SECOND YEAR

	Month	Beginning Balance	Total Payment	Interest	Principle	Ending Balance
	0					$617,195.97
	1	$617,195.97	$4,409.33	$3,471.73	$937.60	$616,258.36
	2	$616,258.36	$4,409.33	$3,466.45	$942.88	$615,315.48
	3	$615,315.48	$4,409.33	$3,461.15	$948.18	$614,367.30
	4	$614,367.30	$4,409.33	$3,455.82	$953.52	$613,413.79
	5	$613,413.79	$4,409.33	$3,450.45	$958.88	$612,454.91
	6	$612,454.91	$4,409.33	$3,445.06	$964.27	$611,490.63
	7	$611,490.63	$4,409.33	$3,439.63	$969.70	$610,520.93
	8	$610,520.93	$4,409.33	$3,434.18	$975.15	$609,545.78
	9	$609,545.78	$4,409.33	$3,428.70	$980.64	$608,565.15
	10	$608,565.15	$4,409.33	$3,423.18	$986.15	$607,578.99
	11	$607,578.99	$4,409.33	$3,417.63	$991.70	$606,587.29
	12	$606,587.29	$4,409.33	$3,412.05	$997.28	$605,590.01
	Loan balance at the end of Year 3	$605,590.01

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