0.96.
To best compute this problem, use your financial calculation to input the initial outflow (investment) of $38,000 and the four cash inflows ($12,000 in each of Yr 1, 2, and 3, and $6,500 in Yr 4). Then use the NPV calculation with the 7% discount rate to find the NPV for the project of -$1,549.
Using this NPV along with the initial investment, compute the profitability index by adding the NPV and the initial investment then dividing this sum by the initial investment.
profitability index = (NPV + initial investment) / initial investment
0.96 = (-$1,549 + $38,000) / $38,000