1. **State the problem:** Verify the monthly difference in investment needed so that Stephanie and Seamus each receive 34000 at age 21, given a 4.2% annual interest compounded monthly. 2. **Recall the formula for future value of an ordinary annuity:** $$FV = P \times \frac{(1+i)^n - 1}{i}$$ where $P$ is the monthly payment, $i$ is the monthly interest rate, and $n$ is the number of months. 3. **Calculate monthly interest rate:** $$i = \frac{4.2\%}{12} = 0.0035$$ 4. **Calculate months until 21 for each child:** - Seamus: $21 - 3.3333 = 17.6667$ years $\Rightarrow n_S = 17.6667 \times 12 = 212$ months - Stephanie: $21 - 6.5 = 14.5$ years $\Rightarrow n_{St} = 14.5 \times 12 = 174$ months 5. **Calculate annuity factors:** $$(1+i)^{212} = (1.0035)^{212} \approx 2.096$$ $$(1+i)^{174} = (1.0035)^{174} \approx 1.835$$ 6. **Calculate denominators:** $$D_S = \frac{2.096 - 1}{0.0035} = \frac{1.096}{0.0035} \approx 313.14$$ $$D_{St} = \frac{1.835 - 1}{0.0035} = \frac{0.835}{0.0035} \approx 238.57$$ 7. **Calculate monthly payments:** $$P_S = \frac{34000}{313.14} \approx 108.56$$ $$P_{St} = \frac{34000}{238.57} \approx 142.48$$ 8. **Calculate difference:** $$142.48 - 108.56 = 33.92$$ 9. **Check for possible rounding or input differences:** If the answer 30.02 is given, it may be due to slightly different assumptions or rounding in interest rate or time periods. **Final answer:** Benny must invest approximately **33.92** more per month for Stephanie than for Seamus to ensure both receive 34000 at age 21.