$4)$ You take out a $5/130-$year ARM for $$625,750$ with an intial rate of $5\mathrm{.}5\%.$ It is indexed to the $10-$year Treasury rate with a margin of $1\mathrm{.}75\%.$

The $10-$year Treasury rate for the first $7$ years are: Year $14\mathrm{.}50\%$ Year $24\mathrm{.}25\%$ Year $34\mathrm{.}75\%$ Year $45\mathrm{.}00\%$ Year $54\mathrm{.}00\%$ Year $63\mathrm{.}50\%$ Year $73\mathrm{.}00\%$

a$)$ What is the effective rate for this loan?

b$)$ What is the effective rate for this loan if closing costs are $$5,000?$

c$)$ If you sell your house and pay off your loan at the end of year $7,$ what is the effective rate you paid over the first $7$ years? Include fees from b$)$