1. **State the problem:** We need to solve for the principal amount $P$ in the equation $$27660 = P(1 + 6.7\%)^5.$$ 2. **Convert the percentage to decimal:** $$6.7\% = 0.067.$$ So the equation becomes $$27660 = P(1 + 0.067)^5 = P(1.067)^5.$$ 3. **Calculate $(1.067)^5$:** $$1.067^5 = 1.067 \times 1.067 \times 1.067 \times 1.067 \times 1.067.$$ Using a calculator, $$1.067^5 \approx 1.38368.$$ 4. **Rewrite the equation:** $$27660 = P \times 1.38368.$$ 5. **Solve for $P$ by dividing both sides by 1.38368:** $$P = \frac{27660}{1.38368} \approx 19984.68.$$ **Final answer:** $$\boxed{P \approx 19984.68}.$$ This means the initial principal amount is approximately 19984.68.