Explanation:

- Announce: This refers to making a public or formal statement about something. It doesn't fit here as the context suggests showing off wealth, not just stating it.

- Claim: This implies asserting something as a fact. It doesn't quite match because it lacks the aspect of showing off or expressing pride.

- Boast: This word is about talking with excessive pride and self-satisfaction, especially about achievements or possessions. In the context of showing off riches, this fits perfectly.

- Pretend: This means making something appear true when it is not. Here, it doesn’t work well because it involves deceit, not prideful display.