1. **State the problem:** Calculate the value of $1.005^{96}$. 2. **Formula used:** The expression is an exponentiation where the base is $1.005$ and the exponent is $96$. 3. **Explanation:** To solve $1.005^{96}$, we multiply $1.005$ by itself $96$ times. 4. **Intermediate work:** Using a calculator or computational tool, we find: $$1.005^{96} \approx 1.005^{100} \times 1.005^{-4}$$ Since $1.005^{100} \approx 1.6487$ and $1.005^{-4} \approx 0.9802$, multiplying these gives: $$1.6487 \times 0.9802 \approx 1.616$$ 5. **Final answer:** $$\boxed{1.616}$$