1. **State the problem:** Declan invested some prize money in a savings account with compound interest at 8% per annum. After 14 years, the amount in the account is 14685.97. We need to find the initial investment amount. 2. **Formula used:** The compound interest formula is: $$A = P \times (1 + r)^t$$ where: - $A$ is the amount after time $t$ - $P$ is the principal (initial investment) - $r$ is the annual interest rate (as a decimal) - $t$ is the time in years 3. **Given values:** - $A = 14685.97$ - $r = 0.08$ - $t = 14$ 4. **Rearrange the formula to find $P$:** $$P = \frac{A}{(1 + r)^t}$$ 5. **Calculate $(1 + r)^t$:** $$1 + r = 1 + 0.08 = 1.08$$ $$1.08^{14} = 2.937686$$ (rounded to 6 decimal places) 6. **Calculate $P$:** $$P = \frac{14685.97}{2.937686}$$ 7. **Show cancellation step:** $$P = \frac{\cancel{14685.97}}{\cancel{2.937686}}$$ (just indicating division) 8. **Perform division:** $$P \approx 5000.00$$ 9. **Final answer:** Declan initially invested approximately **5000** (to the nearest 1).