Consider a $$5,000,000,25-$year ARM with monthly payments and annual interest adjustments. The initial interest rate is $6\mathrm{.}5\%.$ The index for the loan is $1-$year US Government bonds, currently yielding $5\%.$ The loan has a margin of $200$ basis points.

$($a$)$ Is the loan$$s initial interest rate a $$teaser rate$?$ How do you know?

$($b$)$ If $1-$year T$-$bonds remain at $5\%,$ what will be the applicable interest rate for this mortgage after the first year?

$($c$)$ What are the initial monthly payments on this loan?

$($d$)$ Assuming T$-$Bonds remain at $5\%,$ what will be the monthly payments after the first year?

$($e$)$ Under that assumption $($and assuming no discount points$),$ what is the forecasted yield to$-$maturity on this loan at the time it is issued.