Kyle purchased a $$4,000$ bond that was paying a coupon rate of $5\mathrm{.}90\%$ compounded semi$-$annually and had $5$ more years to mature. The yield at the time was $6\mathrm{.}40\%$ compounded semi$-$annually.

a$)$ How much did Kyle pay for the bond?

b$)$ What was the amount of premium or discount on the bond?