1. **Problem statement:** Calculate the total value of Fiona's pension fund after saving €120 weekly for 25 years at an annual interest rate of 3.9%. 2. **Formula used:** The future value of an annuity formula is $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. 3. **Given:** - Weekly payment $P = 120$ - Annual interest rate $= 3.9\%$ - Number of years $= 25$ - Number of weeks per year $= 52$ 4. **Calculate weekly interest rate:** $$r = \frac{3.9}{100} \div 52 = 0.00075$$ 5. **Calculate total number of payments:** $$n = 25 \times 52 = 1300$$ 6. **Calculate future value:** $$FV = 120 \times \frac{(1 + 0.00075)^{1300} - 1}{0.00075}$$ 7. **Calculate $(1 + 0.00075)^{1300}$:** $$ (1.00075)^{1300} \approx e^{1300 \times \ln(1.00075)} \approx e^{1300 \times 0.00075} = e^{0.975} \approx 2.6533$$ 8. **Substitute back:** $$FV = 120 \times \frac{2.6533 - 1}{0.00075} = 120 \times \frac{1.6533}{0.00075}$$ 9. **Simplify:** $$FV = 120 \times 2204.4 = 264,528$$ **Final answer:** Fiona's pension fund will be approximately **264,528 euros** after 25 years.