Question

A basic ARM is made for $250, 000 at an initial interest rate of 6% for 30 years with an annual reset date. The borrower believes that the interest rate at the beginning of year 2 will increase to 8 percent.

a. Assuming that a fully amortizing loan is made. What is the monthly payment during year 2?

b. What would be the monthly payments in year 2 if it is an interest-only ARM loan for the first two years?

c. Assuming that fulling amortizing is made and negative amortization is allowed if payment cap reached. If the ARM loan has a maximum 5% annual increase payment cap, what is the monthly payment during year 2?

Answer 1

	Adjustable rate mortgage
	Principal amount	Rate	Period
	$2,50,000	6%	30 years with annual reset date
	Interest rate may increase to 8% from the beginning of year 2
(a)	Assuming a fully amortizing loan is made, Montly payment in year 2
	Monthly payment in year 1				Loan amortisation schedule
	L	i(1+i)n	(1+ i)n-1		(a)	(b)	© - as computed	(d) = (b)*6%*1/12	(e) = © - (d)
	$2,50,000	0.005 (1+0.005)360	(1+0.005)360-1		Month	Principal Amount	Repayment amount	Interest @ 6% per month	Towards Principal
		0.030112876	5.022575212		1	$2,50,000	$1,499	$1,250	$249
		0.005995505			2	$2,49,751	$1,499	$1,249	$250
		$1,498.88			3	$2,49,501	$1,499	$1,248	$251
	Monthly payment = L * ((i (1+ i)n /(1+ i)n-1)				4	$2,49,249	$1,499	$1,246	$253
					5	$2,48,997	$1,499	$1,245	$254
	L = Loan amount				6	$2,48,742	$1,499	$1,244	$255
	i = Monthly interest rate = 6%/12 =0.5% for 12 months = 0.5/100=0.005				7	$2,48,487	$1,499	$1,242	$257
	n = Number of months in loan - 30 years * 12 months				8	$2,48,231	$1,499	$1,241	$258
					9	$2,47,973	$1,499	$1,240	$259
	Monthly payment in year 2 - Interest rate in year 2 @ 8%				10	$2,47,714	$1,499	$1,239	$260
					11	$2,47,453	$1,499	$1,237	$262
	$2,46,928	Loan amount as per amortisation schedule (L)			12	$2,47,191	$1,499	$1,236	$263
	0.08/12	0.006666667	Interest rate per month (i)			Total	$17,988	$14,916	$3,072
	29*12	348.00	number of months (n)		13	$2,46,928
	Monthly payment
	246928.4	0.0067(1+0.0067)348	(1+0.0067)348-1
		0.068438216	9.214659089
		$1,833.96

(b)	Monthly payment in year 2 - if interest only ARM for first two years
	8% interest in year 2
	Loan OS amount in year2 will be $ 250000 as payment made towards interest only in year 1
	therefore, monthly payment will be
	$ 250,000 * 8% * 1/12
	$1,666.67