Question

A borrower is offered a 30 year, fully amortizing ARM with an initial rate of 3.2%. After the first year, the interest rate will adjust each year, using 1 yr LIBOR as the index, plus a margin of 175bp. The price of the property is $8,000,000 and the loan will have an initial LTV ratio of 75% At the first reset date, 1 year LIBOR is at 3%. What is the borrower’s payment during the 2nd year of the loan?

Answer 1

Given LTV Ratio =75%
Property Price =$8,000,000
Loan Amount =$8M*75% =	$                6,000,000
Loan period =30 years =360 months
Interest rate in 1st year =3.2% pa=	0.2667%	per month

Assume the Balance Principal after 1st year =B
The next formula is used to calculate the remaining loan balance (B) of a fixed payment loan after p months
B = P[(1 + i)^n - (1 + i)^p]/[(1 + i)^n - 1]
Here P=6,000,000
i=0.2667% per month
n=360 months
p=12 months
B=6,000,000*[1.002667^360-1.002667^12]/(1.002667^360-1)
B =$5,878,865.50
So Balance Principal after 1 year =	$          5,878,865.50

Interest rate for 2nd year installment calculation
1 Year LIBOR =3%
Margin 175bp=1.75%
So Effective Interesr rate for 2nd year=4.75% pa
So Effective Interesr rate for 2nd year=0.3958% per month
Formula for loan amortization =
A= [i*P*(1+i)^n]/[(1+i)^n-1]
A = periodical installment=??
P=Loan amount =$5,878,865.50
i= interest rate per period =0.3958% per month
n=total no of payments=29 years=348 months
A= 0.3958%*5878865.5*[1.003958^348]/(1.003958^348-1)
A =$31,148.79
So Monthly Installment during second year =	$               31,148.79