The 4.35% Is an Average, Not a Promise
The prize fund rate is the total value of prizes paid out as a share of all eligible Bonds in a year. NS&I states the odds plainly: 21,000 to 1 for every £1 Bond, every month, variable. That is better than the 23,000 to 1 of the April draw, but it is still a lottery ticket, not a savings rate.
September's draw shows what the average hides. NS&I paid £497,086,175 across 6,529,868 prizes. Two people won £1 million. Ninety-five won £100,000.
Now look at the bottom of the distribution: 6,446,807 of the 6,529,868 prizes — 98.7% — were worth £100 or less. The two £1 million jackpots that make 4.35% mathematically true are two tickets out of 6.5 million.
The honest way to think about Premium Bonds is the median, not the mean. A holder with £1,000 might win nothing for months. A holder with the full £50,000 can expect the mean to assert itself over time, but the distribution stays right-skewed — a handful of big wins, millions of £25s.