在新概念英语见过 was determined to do和determined to do用法：

    I have been offered a large sum of money to go away， but I am determined to stay here. Everybody says I must be mad and they are probably right（他们曾向我提供一大笔钱让我搬走，但我决定留在这儿。大家都说我肯定是疯了，也许他们说的是对的。）在这里作者用determined表达了一种态度，一种“决定”想法，有点“一时冲动的决定”味道，到时候说不定还是要离开，因为后边的那句话埋下伏笔。

   I determined to lodge a complaint as soon as we arrived. Two hours later， I was talking angrily to the station master at Westhaven.（我决定到目的地就给铁路部门提意见。两小时后，我气呼呼地同威斯特海温站站长说起此事。）在这里用determined用的很贴切，表达了要去到目的地就给铁路部门提意见的决心，果然，后句就说明了这一点：两小时后，我气呼呼地同威斯特海温站站长说起此事

问题中 He determined to get the reward，表达了Mr. Budd决心要获得这笔钱的坚强决心，而且一定能办到。