Question

Compute the payment for year 2 for the following adjustable rate mortgage. The loan has an annual adjustment period, is indexed to the one-year Treasury Bill, and carries a margin of 2%. The original composite rate was not a teaser and was equal to 4%. The one-year T-bill rate decreased 0.5% at the start of year 2. The loan was 80% loan-to-value on a property worth $220,000, and it was fully amortizing over a term of 30 years.

Answer 1

First year:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          176,000
Rate of interest per period:
Annual rate of interest		4.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.04 /12 =	0.3333%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 176000 × 0.00333 × (1+0.00333)^360] / [(1+0.00333 ^360 -1]
Monthly payment	=	$                                                            840.25

Balance after one year:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	176,000.00
Rate of interest	r=	0.3333%
nth payment	n=	12
Payment	P=	840.25
Loan balance	=	176000*(1+0.00333)^12 - 840.25*[(1+0.00333)^12-1]/0.00333
Loan balance	=	172,900.59

Rate for second year = 4% - 0.5% = 3.5% (t bill rate declined).

Monthly payment is:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          172,901
Rate of interest per period:
Annual rate of interest		3.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.035 /12 =	0.2917%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	29
Total number of payments	N	29 × 12 =	348
Period payment using the formula	=	[ 172900.59 × 0.00292 × (1+0.00292)^348] / [(1+0.00292 ^348 -1]
Monthly payment	=	$                                                            791.59

Second year monthly payment is $791.59