According to the PMBOK® Guide, specifically within the Monitor and Control Project Work process, the Schedule Performance Index (SPI) is a measure of schedule efficiency expressed as the ratio of earned value to planned value.

The Formula: The SPI is calculated using the following equation:

$$SPI = \frac{EV}{PV}$$

The Calculation:

Given Earned Value ($EV$) = $30$

Given Planned Value ($PV$) = $15$

$SPI = \frac{30}{15} = 2.0$

Interpreting the Result:

SPI > 1.0: Indicates that more work was completed than was originally planned. The project is ahead of schedule.

SPI < 1.0: Indicates that less work was completed than was planned. The project is behind schedule.

SPI = 1.0: Indicates that the project is exactly on schedule.

Context: An SPI of $2.0$ means the project team is performing at $200\%$ efficiency relative to the schedule. For every hour of work planned, two hours ' worth of work (in terms of value) has been accomplished.

Analysis of other options:

Option B (45): This is the result of adding $EV$ and $PV$ ($30 + 15$), which has no standard meaning in Earned Value Management.

Option C (0.5): This is the result of dividing $PV$ by $EV$ ($15 / 30$). This is the inverse of the SPI formula and is incorrect.

Option D (15): This is the result of $EV - PV$ ($30 - 15$), which is the formula for Schedule Variance (SV), not the index.

Per PMI standards, the Schedule Performance Index (SPI) is a critical metric for determining the efficiency of the project team ' s use of time, and in this specific case, the value of 2.0 indicates exceptionally high schedule performance.