You bought a newly issued $10-$year, $$1,000$ par value, $5\mathrm{.}50\%$ coupon bond $($with semiannual coupon payments$)$ on May $1,2023.$ You decided to check the value and yields on the bond annually, so that you can keep track of your wealth. Your first check was to be done on May $1,2024.$ On April $15,2024,$ the yield to maturity for the bond changed to $5\mathrm{.}20\%.$

For your two year anniversary of owning the bond $($May $1,2025),$ calculate the bond's capital gains yield for the second year of ownership.