Darians IRA has fallen 12.6% to 142,500.49. What was the value of her IRA at the beginning of the year?

So it is now 87.4% of what it was before.

.874x = 142500.49
x = 142500.49/.874 = 163 044.39

0.874x = 142,500.49

Solve for x.

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.