Question

A borrower is offered a 30 year, fully amortizing ARM with an initial rate of 3.35%. 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

Initial Interest Rate = 3.35%, Tenure = 30 years, Property Price = $ 800000, LTV = 75 %

Mortgage Amount = LTV x Property Price = 0.75 x 800000 = $ 600000

Let the first annual repayment be $ p (this will be calculated using the initial interest rate)

Therefore, 600000 = p x (1/0.0.0335) x [1-{1/(1.0335)^(30)}]

600000 = p x 18.742621

p = 600000 / 18.742621 = $ 32012.598

Interest Expense for Year 1 = Mortgage Outstanding at the beginning of Year 1 x Interest Rate for Year 1 = 600000 x 0.0335 = $ 20100

Principal Repaid in Year 1 = 32012.598 - 20100 = $ 11912.598

Principal Outstanding at the Beginning of Year 2 = 600000 - 11912.598 = $ 588087.4

Interest Rate during Year 2 = LIBOR at the beginning of year 2 + Margin = 3 + 1.75 = 4.75 %

Year 2 Repayment will be calculated using the Year 2 interest rate and the remaining mortgage balance.

Let the year 2 payment be $m

Therefore, 588087.4 = m x (1/0.0475) x [1-{1/(1.0475)^(29)}]

588087.4 = m x 15.571888

m = 588087.4 / 15.571888 = $ 37765.966 ~ $ 37765.97

Interest Portion of Second Repayment = Mortgage Outstanding at the Beginning of Year 2 x Interest Rate for Year 2 = 588087.4 x 0.0475 = $27934.12