John invests $1,000$ in a fund which earns interest during the first year at a nominal rate of K convertible quarterly. During the second year, the fund earns interest at a nominal discount rate of K convertible semi$-$annually. At the end of the second year, the fund has accumulated to $1,174\mathrm{.}51.$

Calculate $K.$

a $0\mathrm{.}080$

b $0\mathrm{.}182$

C $0\mathrm{.}200$

d $0\mathrm{.}068$

e $0\mathrm{.}064$