I did not know until now that the other 20% could be reclaimed by the donor as well, if they paid 40% tax.
If the donor donates that amount as well and we loop infinitely, the final amount received by the charity would be exactly 1.5625x the originally-donated amount (assuming that the HMRC allows arbitrary small fractions of a penny to be claimed).
Explanation: if you donate an amount x, the final amount would be the infinite series x + sigma(0.25*0.2^(k-1) + 0.2^k, k=1, k=inf), which is the sum of two separate geometric series, so for each one, we can use the formula a/(1-r), where 'a' is the first term (0.25 for the first series, 0.2 for the second) and 'r' is the ratio between each term (0.2 in both cases).
If the donor donates that amount as well and we loop infinitely, the final amount received by the charity would be exactly 1.5625x the originally-donated amount (assuming that the HMRC allows arbitrary small fractions of a penny to be claimed).
Explanation: if you donate an amount x, the final amount would be the infinite series x + sigma(0.25*0.2^(k-1) + 0.2^k, k=1, k=inf), which is the sum of two separate geometric series, so for each one, we can use the formula a/(1-r), where 'a' is the first term (0.25 for the first series, 0.2 for the second) and 'r' is the ratio between each term (0.2 in both cases).