1. **State the problem:** We want to find the daily savings amount needed to accumulate $52200$ over 4 years with daily compounding interest at an annual rate of 4.6%. 2. **Formula used:** The future value $FV$ of a sinking fund with regular payments $P$ compounded daily is given by: $$FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}$$ where: - $r = 0.046$ (annual interest rate) - $n = 365$ (compounding periods per year) - $t = 4$ (years) 3. **Rearrange to solve for $P$:** $$P = \frac{FV \times (r/n)}{(1 + r/n)^{nt} - 1}$$ 4. **Calculate intermediate values:** - $r/n = \frac{0.046}{365} \approx 0.000126027$ - $nt = 365 \times 4 = 1460$ 5. **Calculate $(1 + r/n)^{nt}$:** $$ (1 + 0.000126027)^{1460} \approx e^{1460 \times \ln(1.000126027)} \approx e^{1460 \times 0.00012602} \approx e^{0.1839} \approx 1.2019 $$ 6. **Calculate denominator:** $$1.2019 - 1 = 0.2019$$ 7. **Calculate numerator:** $$52200 \times 0.000126027 = 6.5774$$ 8. **Calculate daily payment $P$:** $$P = \frac{6.5774}{0.2019} \approx 32.56$$ **Final answer:** The undergraduate needs to save approximately **32.56** each day to afford the median cost of a masters degree after 4 years.