LarryScott
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The interest rate on Prize Bonds is 0%. There is a chance you might get a prize but they are, in essence, raffle tickets. Most people never see a return, just an asset with a reducing value year on year due to inflation.
There is an argument that the really low probability prizes aren't really relevant when working out investment return.
The 2024 number from the table give these results
| Prize | Count | Paid Out |
| 500000 | 12 | 6,000,000.00 |
| 50000 | 52 | 2,600,000.00 |
| 1000 | 1040 | 1,040,000.00 |
| 500 | 1040 | 520,000.00 |
| 75 | 472958 | 35,471,850.00 |
| Total | 45,631,850.00 | |
| Funds (1%) | 4,563,185,000.00 |
If you invested 100k in prize bonds, then you get (100k)/(4.563 billion) =0.00002191 of the entire fund.
You can fill that into the table (all counts gets multiplied by 0.00002191).
| Prize | Count | Paid Out |
| 500000 | 0.000263 | 131.5 |
| 50000 | 0.00114 | 57 |
| 1000 | 0.0228 | 22.8 |
| 500 | 0.0228 | 11.4 |
| 75 | 10.365 | 777.38 |
| Total | 1000 |
100k gives 1000 (1%) per year on average, including contributions from the high prizes.
However, in practice you are really unlikely to get a 500k or 50k payout (odds of 0.000263 and 0.00114). Even with a 50 year horizon that is still pretty unlikely.
From an investing viewpoint, this is pure gambling rather than having much hope of getting that return. The 1000 and 500 prizes are also low chance. You get one or other of them every 22 years. Maybe with long term 30-40 investment time-frames you could include those.
In practice, only the 75 prizes are reliable enough to consider for investment return. You should get roughly the expected payout in that case.
This reduce the return from prize bonds from 1% to around 0.777%. That is return that also everyone who has prize bonds actually gets.
The average is still 1%, but that is due to being pushed up by lucky people.
Seems a bit confusing...
Are they saying that it is deterministic? You could work out the numbers for the next year if you knew the rule?
If that is true, then someone who knew the algorithm could buy bonds, see if they win, and then return them if they are losers.