1. **State the problem:** Calculate the amount $A$ using the formula for continuous compound interest: $$A = \phi e^{rt}$$ where $\phi = 100$, $r = 0.05$, and $t = 3$ years. 2. **Formula explanation:** This formula calculates the amount $A$ after time $t$ when interest is compounded continuously at rate $r$ on principal $\phi$. 3. **Substitute the values:** $$A = 100 \times e^{0.05 \times 3}$$ 4. **Calculate the exponent:** $$0.05 \times 3 = 0.15$$ So, $$A = 100 \times e^{0.15}$$ 5. **Evaluate $e^{0.15}$:** Using a calculator or approximation, $$e^{0.15} \approx 1.16183424$$ 6. **Calculate $A$:** $$A = 100 \times 1.16183424 = 116.183424$$ 7. **Final answer:** $$\boxed{116.18}$$ The amount after 3 years with continuous compounding at 5% interest on 100 principal is approximately 116.18.