Question

You have taken out a $100,000, one-year ARM. The teaser rate in the first year is 4.5% (annual). The index interest rate after the first year is 3.25% and the margin is 2.75%. (Note: The term on this ARM is 30 years). There is also a periodic (annual) rate cap of 1.00%. Given this information, determine the monthly mortgage payment you would be scheduled to make in month 13 of the mortgage loan's term. A) $321.64 B) $566.26 C) $506.69 D) $597.21

Answer 1

Mortgage =$ 100000, Year 1 Teaser Rate = 4.5 % and Mortgage Tenure = 30 years or 360 months

Monthly Rate during Year 1 = (4.5/12) = 0.375 %

Let the monthly repayments be $P

Therefore, 100000 = P x (1/0.00375) x [1-{1/(1.00375)^(360)}]

100000 = P x 197.3612

P = 100000 / 197.3612 = $ 506.68

Principal Outstanding after Year 1 = PV of Remaining Monthly Repayments discounted at the initial teaser rate of 4.5 % = 506.68 x (1/0.00375) x [1-{1/(1.00375)^(348)}] = $ 98386.77

At the end of Year 1, the applicable interest rate changes to the floating rate. Floating Rate is determined by adding the given margin to the index interest rate.

Index Interest Rate = 3.25 % and Margin = 2.75 %

Applicable Interest Rate = 3.25 + 2.75 = 6 %

However, there is cap on the periodic rate of 1 % per annum, which essentially implies that the periodic rate cannot change by more than 1 % from one period to another. Hence, the Year 2 rate will not be more than (4.5 + 1) = 5.5 %

Hence, applicable interest rate for beginning of Year 2 = 5.5 %

Applicable Monthly Rate = 5.5 / 12 = 0.4583 %

Let the new monthy repayment be $ K

Therefore, 98386.77 = K x (1/0.004583) x [1-{1/(1.004583)^(348)}]

98386.77 = K x 173.7568

K = 98386.77 / 173.7568 = $ 566.2328 ~ $ 566.26

Hence, the correct option is (B)