Question $2$: Forecasting ARM rates Question $(30$ points$)$

Adjustable$-$rate mortgage amortized over $30$ years, with an LTV of $80\%$ and a $4\mathrm{.}50\%$ teaser rate. The margin rate for this loan is $3\mathrm{.}15\%,$ and the index rate is $4\mathrm{.}00\%.$ Assume the index rate increases to $4\mathrm{.}30\%$ at the beginning of year $3.$ Early repayment charges apply within the first $3$ years of the loan at $2\%$ of the outstanding balance. The property you$$re looking at is priced at $$800,000($ignore acquisition fees$).$

$1.$ What is the interest rate on this loan in the following years $(9$ points$)$:

a$.$ Year $1$

b$.$ Year $2$

c$.$ Year $3$

$2.$ To fill in the table, calculate the monthly payment and the outstanding loan balance of the ARM at the beginning of year $1,$ year $2$ and year $3.(18$ points$)$

Beginning of Year $1$ Beginning of Year $2$ Beginning of Year $3$

Loan Balance

Monthly Payment

$3.$ Calculate the repayment charges if the property was sold after $2$ years. $(3$ points$)$