Lancashire Corp. issued $$400,000$ of $8\%,20-$year bonds at $102.$ Interest is paid semi$-$annually. The market rate for similar investments is $7\%.$

a$.$ What amount was received for the bonds?

b$.$ How much interest is paid each interest period?

c$.$ How much interest expense is recorded on the first interest date?

d$.$ What is the carrying value of the bonds after the first interest date?