when an investment is HTM, and the cost is higher than par, will the B/S carry cost reduced each year until at the maturity, the cost=par? is the reduced amount called Accrued interest or Amort/disc? Thanks.

accrued interest is entirely different and involves the purchase of a fixed income security in between coupon payment periods. under htm the value of the security on the bs will be carried at amortized cost. amortized cost does not equal the par value. for a premium bond, amortized cost equals the original purchase prices less the amortized premium.

you would subtract amortized premium each year until the bond was back to par, yep

The amortization equals Coupon payment - effective interest rate * book value