Percentages involving Finances: Profit and Loss

The value of a machine depreciates by \(50\%\) every year after its purchase. If the value of a machine is \(\$250,000\) in the year \(2020\), and the price was \(\$2,000,000\) on purchase.

1. Find the year when the machine was purchased.
2. Find the year when the machine's value depreciates to \(\$62,500\).