(i) Using Model 1, the prize money increases by $1000 each day, forming an arithmetic series: 1000, 2000, 3000, ..., up to 40 terms.

The sum of an arithmetic series is given by \(S_n = \frac{n}{2} (a + l)\), where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.

Here, \(n = 40\), \(a = 1000\), and \(l = 40000\).

\(S_{40} = \frac{40}{2} (1000 + 40000) = 20 \times 41000 = 820000\).

The total donation is 5% of this sum: \(0.05 \times 820000 = 41000\).

(ii) Using Model 2, the prize money increases by 10% each day, forming a geometric series: 1000, 1000 \(\times 1.1\), 1000 \(\times 1.1^2\), ..., up to 40 terms.

The sum of a geometric series is given by \(S_n = a \frac{r^n - 1}{r - 1}\), where \(a\) is the first term and \(r\) is the common ratio.

Here, \(a = 1000\), \(r = 1.1\), and \(n = 40\).

\(S_{40} = 1000 \frac{1.1^{40} - 1}{1.1 - 1} \approx 442000\).

The total donation is 5% of this sum: \(0.05 \times 442000 = 22100\).