1. **State the problem:** We have an initial value $C_0 = 12000$ and a compound growth formula $C_{n+1} = 1.0062 \times C_n$ with rate $R = 1.0062$. 2. **Formula used:** The compound value after $n$ periods is given by the geometric sequence formula: $$ C_n = C_0 \times R^n $$ where $C_0$ is the initial value, $R$ is the growth rate per period, and $n$ is the number of compounds. 3. **Explanation:** Each new value is obtained by multiplying the previous value by the rate $R$. This means the value grows by a factor of $1.0062$ each period. 4. **Intermediate work:** For example, after 1 compound: $$ C_1 = 12000 \times 1.0062 = 12000 \times 1.0062 $$ After 2 compounds: $$ C_2 = 12000 \times (1.0062)^2 $$ 5. **Summary:** To find the value after $n$ compounds, use: $$ C_n = 12000 \times (1.0062)^n $$ This formula allows you to calculate the compounded value for any number of compounds $n$.