Final answer:
The annuity would realize a growth of 5%.
Step-by-step explanation:
To calculate the growth that the annuity would realize, we need to multiply the growth of the index by the participation rate. In this case, the index grew by 10% and the participation rate is 50%. So the growth realized by the annuity would be:
Growth = Index Growth × Participation Rate
Substituting the values, we get:
Growth = 10% × 50% = 5%
Therefore, the annuity would realize a growth of 5%.