Today you bought a callable bond issued at a yield to maturity of $5\mathrm{.}5\%.$ It has $10$ years to maturity, a coupon rate of $6\%,$ a call price of $106,$ and the first call date is in $3$ years. The yield and coupon follow the convention with semi$-$annual periods. Which of the following is closest to the yield to call $($YTC$)$ on the bond?

Question $7$ options:

a$)$

$6\mathrm{.}92\%$

b$)$

$5\mathrm{.}85\%$

c$)$

$6\mathrm{.}18\%$

d$)$

$6\mathrm{.}53\%$