One type of mortgage is the adjustable rate mortgage (ARM). With an ARM, the interest rate
changes periodically as determined by a measure of current interest rates, called an index. The
most common index in the United States, called the 1-year CMT (constant-maturity Treasury
index has ranged from 1% to about 6.3%). The interest rate on the ARM is reset by adding a fixed
percent called the margin to the index percent. For instance, if the current value of the CMT index
is 3% and the margin is 2.7%, then the adjusted interest rate for the mortgage would be 5.7%. The
margin usually remains fixed for the duration of the loan.
Of the many types of ARMs, we will consider the 5/1 ARM. With this type of mortgage, the
interest rate is fixed for the first five years, and then is readjusted each year depending on the value
of the index.
1.) Consider a $200,000 5/1 ARM that has a 2.7% margin, is based on the CMT index, and
has 30-year duration. Suppose that the interest rate is initially 5.7% and the value of the
CMT index is 4.5% five years later when the rate adjusts. Assume monthly compounding.
a.) Calculate the monthly payment for the first 5 years.
b.) Calculate the unpaid balance at the end of the first 5 years.
c.) Calculate the monthly payment for the 6th year
