I mentioned I'd prefer to invest a six-figure amount than most five figure amounts in Prize Bonds. Someone asked me what sort of five figure amount would be acceptable. My answer is that you can choose your own odds. Remember, for the purposes of this discussion, we are talking about the odds of achieving an "average" return in a year. Prize Bonds pay out 1.6% of the invested fund in prizes. But since some of that is in very rare high value prizes, you are best depending only on the most numerous €50 prizes, which represent 1.18% of the fund annually. That is what I mean by the average return. If you pay 41% DIRT this is equivalent to an APR of 1.99%. If you also pay 4% PRSI it grosses up to 2.14%. (All figures to two decimals).
So the question is what are your odds of getting that 1.18% net return?
These odds are what vary depending on the size of your investment. On page 7 of this thread, I posted this graph:
The idea is that it shows you the chance of winning each particular number of individual €50 prizes for a given investment amount. Here is the same data in tabular form (there are more precise values in the attached .csv file which can be loaded in Excel):
So here's how it works. You have to win an integer number of prizes. You can't win half a prize. So, for any given investment amount, multiply by 1.18% and divide by 50. Round to the nearest integer. This gives you the number of prizes you have to win to get as close as you can to the average return.
Let's take €50k as an example. A 1.18% return is €590. Divide by €50 and round to the nearest integer. This gives us 12 prizes for a return of 1.2%, slightly better than average. So now look at the table above. Each column heading is a number of prizes that you could win in a year. Look at the €50k row. The values to the right of the €50k are the odds of winning that number of prizes. Since we want to win 12 prizes, lets add up the odds of getting
less than 12, and the odds of winning 12
or more will be one minus that number. That's all the columns from 0 to 11. Using my more precise values, they sum to 48.93%. That means I have a 51% chance -- just about evens -- of achieving the average return.
That might be good enough for you, or it might not. It's up to you. Of course, don't ignore that if we include the 11, 10, and 9 columns, it gets us up to an 83% chance of winning at least three quarters of an average return. It's never all or nothing. And, of course, you have a non-negligible chance of winning
more than the average return (which can be worked out in a similar way). If you want to improve the odds of achieving close to an average, invest more. You can use this approach for any amount in the above tables.
If you look at €100k, you will see that you only have a 49% chance of getting a 1.2% return, no better than the €50k amount. But you have a 90% chance of getting at least three quarters of that (which, as I mentioned earlier, is still better than the net instant access rate, which you have a 95% chance of beating). In general the odds of getting "near" the average improve with higher investments. Taking a glass-half-empty approach (as I tend to), and asking "how likely am I to get a very
poor return?" ... the answer is "much more likely for small investments". As an extreme example, you can see that for €10k or €5k (and even more so for any amounts less than that) there is a substantial chance of winning nothing at all! (But, as I always point out, if you can wait decades or centuries, you'll still get your 1.18% eventually. Indeed, if you can wait millennia, you'll get your 1.6%).
EDIT: not sure how to do an attachment, so here's the csv data on PasteBin.
EDIT2: For the best net instant access rate for €100k I have been using the PTSB rate from the Best Buys thread of 2% on the first €50k and 1% thereafter. Deducting 45% tax from this give an average net rate of 0.825%. I see that there is a slightly better KBC rate which nets out to 1.01%, which affects my figures marginally. (I also see a Rabo 90 day notice rate which I must take up myself ... thanks as always, Ciaran T!)