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I know that the amount most holders will win on Premium Bonds is actually lower than the quoted "interest rate" (as described here) and I know that the smallest prize is something like £50, but I can't work out how long I should expect to wait for a prize on £100 worth of bonds.

I've held £100 for me and £100 for my son for over 5 years now and not won anything at all. I think this is well within the expected bounds, but I'm curious as to how long the expected wait would be, probability-wise.

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The probability of a single £1 bond winning a prize in any given month are 1/24000 (see http://www.nsandi.com/products/pb/rates - the linked terms and conditions say that a bond unit is £1).

Ignoring the small probability of two or more bonds winning in the same month, that makes the probability of a win in a single month from £100 of bonds equal to 1/240. So, at current interest rates, the expected wait is 20 years.

However since the probability of winning varies with interest rates, which are currently quite low by historical standards, the real expected wait from now is probably lower.

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