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

jeff jeffy answered 2 years ago

An Adjustable Rate Mortgage (ARM) is made for $300,000 at an initial interest rate of 2...

An Adjustable Rate Mortgage (ARM) is made for $300,000 at an initial interest rate of 2 percent for 30 years. The ARM will be adjusted annually. The borrower believes that the interest rate at the beginning of the year (BOY) 2 will increase to three percent (3%). a. Assuming that the ARM is fully amortizing, what will monthly payments be during year 1? b. Based on (a) what will the loan balance be at the end of year (EOY) 1?...

Sharon borrows an adjustable rate loan (ARM) of $100,000 with 3 year loan maturity. The initial...

Sharon borrows an adjustable rate loan (ARM) of $100,000 with 3 year loan maturity. The initial interest rate for the loan is 8.5%, the margin is 3%, the loan amortization period is 15 years, the frequency of adjustment is 1 year (monthly compounding), There will be a discount point of 3% for the loan. Also, the index rates for the next 2 years are 11% and 8%, respectively. NOW suppose there is an annual interest rate cap of 2% specified...

George secured an adjustable-rate mortgage (ARM) loan to help finance the purchase of his home 5...

George secured an adjustable-rate mortgage (ARM) loan to help finance the purchase of his home 5 years ago. The amount of the loan was $250,000 for a term of 30 years, with interest at the rate of 9%/year compounded monthly. Currently, the interest rate for his ARM is 5.5%/year compounded monthly, and George's monthly payments are due to be reset. What will be the new monthly payment? (Round your answer to the nearest cent.)

At the time of origination, the expected yield on an adjustable rate mortgage (ARM) should be...

At the time of origination, the expected yield on an adjustable rate mortgage (ARM) should be less than that of a Fixed Rate Mortgage. Discuss.

The table shows the specifications of an adjustable rate mortgage (ARM). Assume no caps apply. Find...

The table shows the specifications of an adjustable rate mortgage (ARM). Assume no caps apply. Find a) the initial monthly payment; b) the monthly payment for the second adjustment; and c) the change in monthly payment at the first adjustment. *The principal balance at the time of the first rate adjustment. Beginning Balance $75000 Term 20 years Initial index rate 5.4% Margin 2.6 % Adjustment period 1 year Adjusted index rate 6.9% *Adjusted balance $73,414.75 What is the initial monthly...

3. A borrower is unsure whether to go with a fixed rate or adjustable rate loan....

3. A borrower is unsure whether to go with a fixed rate or adjustable rate loan. What kind of questions would you ask to help them decide?

You are considering an adjustable rate mortgage loan with the following characteristics: • Loan amount: $300,000...

You are considering an adjustable rate mortgage loan with the following characteristics: • Loan amount: $300,000 • Term: 20 years • Index: one year T-Bill • Margin: 2.5% • Periodic cap: 2% • Lifetime cap: 5% • Negative amortization: not allowed • Financing costs: $3,500 in origination fees and 1 discount point Suppose the Treasury bill yield is 3.5% at the outset and is then moves to 4.5% at the beginning of the second year and to 8.5% at the...

Assume that the lender offers a 30-year, $150,000 adjustable rate mortgage (ARM) with the following terms:...

Assume that the lender offers a 30-year, $150,000 adjustable rate mortgage (ARM) with the following terms: Initial Interest Rate = 7.5% Index = one-year Treasuries Payments reset each year Margin = 2% Interest rate cap = 1% annually; 3% lifetime Discount points = 2% Fully amortizing; however, negative amortization allowed if interest rate caps reached. Based on estimated forward rates, the index to which ARM is tied forecasted as follows: Beginning of year BOY2 = 7%; BOY3 = 8.5%' BOY4...

You are considering taking out an adjustable rate mortgage (ARM) to finance your new home and...

You are considering taking out an adjustable rate mortgage (ARM) to finance your new home and have been given the following information by the bank: $250,000 house price 80% Loan to Value 200 bps margin 2.5% LIBOR – Index for Year 1 Teaser Rate in Year 1 – 2% Periodic Cap – 1.5% Life Cap – 5% You also went on Bloomberg and found the following LIBOR Index projections for the next few years: 3% - Index for Year 2...

You are looking to finance your home. The bank is offering a three-year ARM (adjustable-rate mortgage)...

You are looking to finance your home. The bank is offering a three-year ARM (adjustable-rate mortgage) with an introductory rate of 3.40%. It has an adjustment cap of 3.00% per adjustment period with a lifetime adjustment of 8.00%. The rate is 4.00% over the one-year LIBOR rate which is currently 1.25%. What will your interest rate be after three years if the LIBOR rate does not change? (Round your answer to 2 decimal places.) In three years, what is the...

Question