Assuming the market is arbitrage-free, if a six-month pure discount bond yields 1.9%, a one-year pure discount bond yields 2.3%, an eighteen-month pure discount bond yields 2.65%, and a two-year discount bond yields 3.05%, what should be the price of a two-year $1,000 6% par-value bond with semiannual coupons?

Answer: $1,057.82

I am required to do problems by hand and also want to understand the steps so please show work.