1. **State the problem:** Calculate the value of the sum $S_4 = 50 \frac{1-0.8^4}{1-0.8}$. 2. **Formula used:** This is the sum of the first 4 terms of a geometric series with first term $a=50$ and common ratio $r=0.8$. The sum formula is: $$S_n = a \frac{1-r^n}{1-r}$$ 3. **Calculate the power:** $$0.8^4 = 0.8 \times 0.8 \times 0.8 \times 0.8 = 0.4096$$ 4. **Substitute values:** $$S_4 = 50 \frac{1 - 0.4096}{1 - 0.8} = 50 \frac{0.5904}{0.2}$$ 5. **Simplify the fraction:** $$\frac{0.5904}{0.2} = \cancel{\frac{0.5904}{\cancel{0.2}}} = 2.952$$ 6. **Multiply by 50:** $$S_4 = 50 \times 2.952 = 147.6$$ **Final answer:** $$S_4 = 147.6$$