Vincent purchased a $$3,500$ bond that was paying a $5\mathrm{.}50\%$ coupon rate and had $4$ more years to mature. The yield at the time of purchase was $4\mathrm{.}20\%$ compounded semi$-$annually.

a$.$ How much did Vincent pay for the bond?

Round to the nearest cent

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