on january 1, 2014, tong purchased a ten-year bond bought at par to yield an annual nominal rate of 5% convertible semiannually. the bond pays semiannual coupons. because tong is an actuary, he enjoys calculating duration as a hobby. tong calculated the duration of the bond as x on january 1, 2016 before the coupon was paid on that date. calculate annualized x.
