Question

You are looking to finance your home. The bank is offering a three year ARM with an introductory rate of 4.50%. It has an adjustment cap of 3.00% per adjustment period with a lifetime adjustment of 7.00%. The rate 3.00% over the one year LIBOR rate which is currently 1.70%.

a. What will your interest rate be after three years if the LIBOR rate does not change. (round to two decimals)

b. In three years, what is the maximum interest rate you could be charged? ( round to two decimals)

c. If LIBOR increases 1.00% per year for the next 10 years up to 11.70%, what is the maximum interest rate you will pay? ( round to two decimals)

Answer 1

Solution:

a) Interest rate after three years:

Interest rate = 1.7%(LIBOR) + 3% = 4.7%.

So, answer is 4.70%

b) Maximum interest rate in three year period:

Maximum interest rate = 4.5% + 3% = 7.5%.

So, answer is 7.50%.

c) Maximum interest rate:

1) 1st Adjustment after 3 years i.e at beginning of year 4:

Libor + 3% = [1.7% + (3x1%)] + 3% = 7.7%

Prior rate + Maximum adjustment = 4.5% + 3% = 7.5%

Lower of the above two rates i.e. 7.5% will be the interest rate charged.

2) 2nd Adjustment after 6 years i.e at beginning of year 7:

Libor + 3% = [1.7% + (6x1%)] + 3% = 10.7%

Prior rate + Maximum adjustment = 7.5% + 3% = 10.5%

Introductory rate + Maximum lifetime adjustment = 4.5% + 7% = 11.5%

Lower of the above three rates i.e. 10.5% will be the interest rate charged.

3) Adjustment after 9 years i.e at beginning of year 10:

Libor + 3% = [1.7% + (9x1%)] + 3% = 13.7%

Prior rate + Maximum adjustment per period= 10.5% + 3% = 13.5%

Introductory rate + Maximum lifetime adjustment = 4.5% + 7% = 11.5%

Lower of the above three rates i.e. 11.5% will be the interest rate charged.

So, Maximum interest rate = 11.50%