It has been quite the roller$-$coaster ride for homeowners in the last year with interest rates steadily increasing. This has caused a lot of stress for those thinking about renewing their mortgage. Bonnie and Clyde find themselves in this situation as they bought a home in their first year of marriage and currently have an outstanding mortgage balance of $$175,000.$ They currently have $14$ months remaining on their mortgage which is at a fixed rate of $4\mathrm{.}5\%$ compounded semi$-$annually on their five$-$year $(60-$month$)$ mortgage term. The current five$-$year fixed rate of interest for a mortgage is $3\mathrm{.}1\%,$ compounded semi$-$annually. Since interest rates are now slightly lower, they would like to $$blend and extend$$ their existing mortgage for another five$-$year term. What rate would they be charged under a blend$-$and$-$extend option?

Select one:

a$.$

$4\mathrm{.}01\%$

b$.$

$3\mathrm{.}98\%$

c$.$

$3\mathrm{.}80\%$

d$.$

$3\mathrm{.}43\%$

e$.$

$4\mathrm{.}56\%$