Question

Jennifer has just borrowed $100,000 to buy a home on a 30-year, adjustable rate mortgage(ARM). The benchmark index is LIBOR which is currently at 2.5%. Her margin is 2% and the loan has caps of 1% annually, and 5% lifetime. While her initial rate should be 4.5%, the lender has granted her a "teaser" rate of 4% for the first year. Assuming that the periodic cap applies to any initial rate, including the teaser rate, if LIBOR rises 1 1/2% to 4% in one year, then, in her second year, Jennifer's mortgage rate will rise to:

5.5%

5%

7%

6%

4.5%

Answer 1

Mortgage rate (1st year) = LIBOR + margin = 2.5% + 2% = 4.5%

Mortgage rate without cap (2nd year) = LIBOR + margin = 4% + 2% = 6%

However, there is a an annual cap of 1%, which means that the mortgage rate cannot increase by more than 1% in any year. Applying the annual cap, maximum mortgage rate for 2nd year = 4.5% + 1% = 5.5%.

There is also a lifetime cap of 5%, which means that the mortgage rate cannot be more than 5% in any year. Applying the lifetime cap, maximum mortgage rate for 2nd year = 5%

The maximum mortgage rate (with cap) in 2nd year = lower of mortage rate with annual cap and mortgage rate with life time cap

The maximum mortgage rate (with cap) in 2nd year = lower of 5.5% and 5%

The maximum mortgage rate (with cap) in 2nd year = 5%

In her second year, Jennifer's mortgage rate will rise to 5%