The Bhatts purchased a new home for $$248,000$ with a down payment

of $$47,000.$They obtained a $25-$year adjustable rate mortgage

with the following terms. The interest rate is based on

the$$one$-$year Treasury bill$$rate$,$ which is currently at

$1\mathrm{.}5\%,$ and$$the$$add$-$on rate, which is $3\mathrm{.}5\%.$The

initial rate period is $5$ years, and$$thereafter$$the

interest rate is adjusted once a year and a new monthly mortgage

payment is calculated.a$)$ Determine the$$Bhatts$\text{'}$ initial ARM rate.$$b$)$ Determine the$$Bhatts$\text{'}$ initial monthly payment for

principal and interest.$$c$)$If$,$ after the$5-$year initial rate$$period$,$ the

rate of the$$one$-$year Treasury bill rises to

$3\mathrm{.}0\%.$determine the$$Bhatts$\text{'}$ new ARM rate.