Question

You have taken out a $250,000, one-year ARM. The teaser rate in the first year is 3.75% (annual). The index interest rate after the first year is 2.75% and the margin is 2.50%. (Note: The term on this ARM is 30 years). There is also a periodic (annual) rate cap of 2.00%. Given this information, determine the monthly mortgage payment you would be scheduled to make in month 13 of the mortgage loan's term.

Answer 1

Initial Teaser Rate = 3.75 %, Mortgage Amount = $ 250000, Tenure = 30 years or (30 x 12) = 360 months

Monthly Rate = (3.75/12) = 0.3125 %

Let the initial monthly payments be $ P

Therefore, 250000 = P x (1/0.003125) x [1-{1/(1.003125)^(360)}]

250000 = P x 215.9288

P = 250000 / 215.9288 = $ 1157.789 ~ $ 1157.79

Outstanding Mortgage After 12 months (1 year) = PV of Remaining Monthly Payments = 1157.79 x (1/0.003125) x [1-{1/(1.003125)^(348)}] = $ 245403.3

Index Interest Rate at the end of Year 1 = 2.75 % and Margin = 2.5 %

Therefore, Applicable Interest Rate post Year 1 = 2.75 + 2.5 = 5.25 %

The periodic rate cap is 2 % which implies that the maximum applicable interest rate after year 1 can be (3.75 + 2) = 5.75 %

As the calculated interest rate is 5.25 % (which is less than 5.75 %), the same would be the applicable rate post Year 1

Let the new monthly repayment be $ M

Applicable Monthly Rate = (5.25 / 12) = 0.4375 %

Therefore, 245403.3 = M x (1/0.004375) x [1-{1/(1.004375)^(348)}]

245403.3 = M x 178.5391

M = 245403.3 / 178.5391 = $ 1374.507 ~ $ 1374.51