1. **State the problem:** We want to find the present investment amount $P$ that will grow to $3000$ in 3 years at an interest rate of 5% per year compounded continuously. 2. **Formula used:** For continuous compounding, the amount $A$ after time $t$ is given by: $$A = Pe^{rt}$$ where: - $P$ is the principal (initial investment), - $r$ is the annual interest rate (as a decimal), - $t$ is the time in years, - $e$ is Euler's number (approximately 2.71828). 3. **Rearrange the formula to solve for $P$:** $$P = \frac{A}{e^{rt}}$$ 4. **Substitute the known values:** $$A = 3000, \quad r = 0.05, \quad t = 3$$ So, $$P = \frac{3000}{e^{0.05 \times 3}} = \frac{3000}{e^{0.15}}$$ 5. **Calculate the denominator:** $$e^{0.15} \approx 1.16183424$$ 6. **Calculate $P$:** $$P = \frac{3000}{1.16183424} \approx 2581.98$$ 7. **Final answer:** You should invest approximately **2581.98** now to have 3000 in 3 years with continuous compounding at 5% interest.