A crypto trader has $80,000$ USDT and can earn $8\%$ APY through DeFi staking. They want to maximize $($natural$)$ log utility across two periods $-$ current trading $($period t$)$ and future trading $($period t$+1).$ What's the optimal trading allocation for period t$?$

Question $2$ options:

$40,000$ USDT

$30,000$ USDT

$50,000$ USDT

$20,000$ USDT