1. **Problem statement:** Acme Confectionery pays €20,000 on retirement day and then pays annually for 25 years, each payment increasing by 1% from the previous one. The annual interest rate is 2.4% (AER). We need to find the total amount the company must set aside on retirement day to fund this pension. 2. **Formula and explanation:** This is a geometric series of payments with first payment $P_1 = 20000$, growth rate $g = 1.01$ (1% increase), number of payments $n = 25$, and discount rate $i = 0.024$. The present value $PV$ of such a growing annuity is given by: $$ PV = P_1 + \sum_{k=1}^{n} \frac{P_1 g^k}{(1+i)^k} $$ Since the first payment is at retirement day (time 0), it is not discounted. The sum from year 1 to 25 is a geometric series: $$ S = P_1 \sum_{k=1}^{n} \left(\frac{g}{1+i}\right)^k $$ Using the formula for geometric series sum: $$ S = P_1 \frac{\frac{g}{1+i} (1 - (\frac{g}{1+i})^n)}{1 - \frac{g}{1+i}} $$ 3. **Calculate ratio $r = \frac{g}{1+i} = \frac{1.01}{1.024} \approx 0.986328125$** 4. **Calculate sum $S$:** $$ S = 20000 \times \frac{0.986328125 (1 - 0.986328125^{25})}{1 - 0.986328125} $$ Calculate $0.986328125^{25}$: $$ 0.986328125^{25} \approx 0.7047 $$ So numerator: $$ 0.986328125 \times (1 - 0.7047) = 0.986328125 \times 0.2953 = 0.2912 $$ Denominator: $$ 1 - 0.986328125 = 0.013671875 $$ Therefore: $$ S = 20000 \times \frac{0.2912}{0.013671875} = 20000 \times 21.29 = 425800 $$ 5. **Add the initial payment (not discounted):** $$ PV = 20000 + 425800 = 445800 $$ 6. **Interpretation:** The company must set aside approximately 445,800 on the day of retirement to fund the pension payments. **Final answer:** $$ \boxed{445800} $$