1. **State the problem:** Mr. and Mrs. Roberts want to invest an amount $P$ now at an interest rate of 8.5% per year compounded continuously, so that in 14 years the investment grows to $8000$. 2. **Formula used:** The formula for continuous compounding is: $$A = P e^{rt}$$ where: - $A$ is the amount after time $t$ - $P$ is the initial principal (amount invested) - $r$ is the annual interest rate (as a decimal) - $t$ is the time in years 3. **Identify known values:** - $A = 8000$ - $r = 0.085$ - $t = 14$ 4. **Solve for $P$:** Rearrange the formula to isolate $P$: $$P = \frac{A}{e^{rt}}$$ 5. **Substitute values:** $$P = \frac{8000}{e^{0.085 \times 14}}$$ 6. **Calculate the exponent:** $$0.085 \times 14 = 1.19$$ 7. **Evaluate $e^{1.19}$:** $$e^{1.19} \approx 3.287$$ 8. **Calculate $P$:** $$P = \frac{8000}{3.287}$$ 9. **Simplify with cancellation shown:** $$P = \frac{\cancel{8000}}{\cancel{3.287}} \approx 2433.68$$ 10. **Final answer:** Mr. and Mrs. Roberts should invest approximately **2433.68** now to have 8000 in 14 years with continuous compounding at 8.5% interest.