Solve an inverse geometric finance model

The camera equipment is represented by an annual percentage-change model

\(V_n\) is the equipment value, in dollars, after \(n\) years. The present value is \(V_0\), so each increase in \(n\) is one annual transition

Each year, reducing-balance depreciation is applied at 12.0% of the current value. After 2 years, the value is exactly $12,971.20