1. **State the problem:** Find the principal amount $P$ that will grow to a future value $A = 8104.00$ at a simple interest rate of 7.8% per year over 2 months. 2. **Formula for simple interest:** $$A = P(1 + rt)$$ where $A$ is the future value, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Convert given values:** - Interest rate: $r = 7.8\% = 0.078$ - Time: $t = \frac{2}{12} = 0.166667$ years - Future value: $A = 8104.00$ 4. **Rearrange formula to solve for $P$:** $$P = \frac{A}{1 + rt}$$ 5. **Substitute values:** $$P = \frac{8104.00}{1 + 0.078 \times 0.166667}$$ 6. **Calculate denominator:** $$1 + 0.078 \times 0.166667 = 1 + 0.013000 = 1.013000$$ 7. **Calculate principal:** $$P = \frac{8104.00}{1.013000}$$ 8. **Show cancellation step:** $$P = \frac{\cancel{8104.00}}{\cancel{1.013000}}$$ 9. **Final calculation:** $$P \approx 7999.21$$ **Answer:** The principal is approximately **7999.21**.