A year ago, you bought a bond with a coupon rate of $4\mathrm{.}7\%,$ just after it paid its semiannual coupon. The bond had $22$ years to maturity, a face value of $$1,000$ and a yield to maturity of $3\%.$Shortly after buying the bond, yields changed to $4\mathrm{.}5\%.$ You reinvested the first coupon at the new market interest rate. What is your realized yield if you sell the bond now, one year after buying it$?$