Question

Find the monthly payment in year 2 for the following ARM: First year rate = 5.4%; 2% annual cap, 6% overall cap; 30-year amortization; margin = 3.0%; Treasury index at end of year 1 = 4.2%; loan amount = $164,000.

Answer 1

First year monthly payment:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          164,000
Rate of interest per period:
Annual rate of interest		5.400%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.054 /12 =	0.4500%
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	=	[ 164000 × 0.0045 × (1+0.0045)^360] / [(1+0.0045 ^360 -1]
Monthly payment	=	$                                                            920.91

Balance after 12 payments:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	164,000.00
Rate of interest	r=	0.4500%
nth payment	n=	12
Payment	P=	920.91
Loan balance	=	164000*(1+0.0045)^12 - 920.91*[(1+0.0045)^12-1]/0.0045
Loan balance	=	161,749.93

Second year:

Interest rate = 4.2% + 3% = 7.2% (is within annual 2% cap)

remaining life 29 years.

Monthly payment is:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          161,750
Rate of interest per period:
Annual rate of interest		7.200%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.072 /12 =	0.6000%
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	=	[ 161749.93 × 0.006 × (1+0.006)^348] / [(1+0.006 ^348 -1]
Monthly payment	=	$                                                         1,108.78

Monthly payment for second year is $1,108.78

please rate.