To find the value of Darian's IRA at the beginning of the year, we need to reverse the 12.6% decrease and apply it to the current value.
First, let's calculate the percentage of the original value that represents the 12.6% decrease:
Percentage decrease = 100% - 12.6% = 87.4%
Next, we'll divide the current value by the percentage above to get the original value:
Original value = Current value / (Percentage decrease / 100)
= 142,500.49 / (87.4 / 100)
= 142,500.49 / 0.874
Using a calculator, we can determine the original value of Darian's IRA:
Original value ≈ 162,985.89
Therefore, the value of Darian's IRA at the beginning of the year was approximately $162,985.89.