Answer: He should invest in second bank to get the most interest over the three year period.
Step-by-step explanation:
Here, the principal amount = $15000 and number of years=3
According to the question,
Compound Interest rate in first saving bank = 2.5% a year
Thus, the total amount by the first bank,
= 16153.359375
Therefore compound interest by first bank,

While, Compound Interest rate in second saving bank = 3.8% for 1st year 1% extra for each extra year.
Thus, the total amount by the second bank,
=17263.76688
Therefore compound interest by the second bank,

Since, 
Thus, he will get more interest in second bank than first bank.