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Premium Bonds Calculator Discussion Area
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This article appeared just as I was looking at Premium Bonds attracted by their tax position for higher rate tax payers and the ability to buy them in regular instalments unlike their index-linked savings certificates.
I've posted another thread as I am now completely puzzled on what to do with my £500/month that I intend to invest. Being a higher rate tax payer is a pain.
I read this piece in the Sunday Times with interest. I have no doubt that the clever maths may well be needed to create the database you have outlined but I think there is a far simpler method which requires only the distribution probability of winning a prize for a given stake and the actual average prize awarded - both obtainable from Ernie. Calculating the expectation value is then very straightforward.
Take my own case: I have a £30k stake which should yield 1.15 prizes a month. My own average prize over the last couple of years has been £60 which therefore gives 1.15*60*12= 828 for the year - or 4.6% equivalent for higher rate tax payer. In practice my prize rate has been 1.25 and that brings the higher rate equivalent up to 5%.
For the general case we need the actual average prize - I haven't had time to go and get that but it should be a simple calculation.
As to the odds of winning a million: surely if there is a total of £36bn staked then by simple division for a £30k stake I have 1 in 1.2m chance each month.
OK I pushed myself - using the numbers available from Ernie's website for the prize distibution the forecast average prize for September is almost exactly £76 - so for a £30k stake the expectation value for the year is 1.15 * 76 *12 = £1048 or 3.5% or 5.83% for a higher rate taxpayer.
NB this is the expectation value - what you actually get won't equate to this in practice due to the scarcity of the higher prizes you will likely make a bit less than this unless of course you hit a big one.
In my book that means this is a worthwhile bet despite the impression given in the Sunday Times.
btw I forgot there are 2 prizes of £1m each month so that means I only have to wait 50000 years to be statistically sure I get my prize.
Statistically speaking I am certain to win a million once if I keep my £30k in there for 100000 years.
Maybe I should sup up...
Actually statistically speaking you're not. As the number of draws increases, you're more and more likely to win, but it's actually an exponential curve that asymptotically approaches a probability of 1 as time goes on.
The reason that this is the case can be modelled with, say, dice. You have a 1 in 6 chance of rolling a 6 each time, which means you have a 5/6 chance of not rolling a 6. The chance of rolling 2 dice and getting no 6 is (5/6)^2, and this extends to the general case of:
P(No 6 in N dice) = (5/6)^N
Or, to rephrase:
P(1 or more 6s in N dice) = 1 - (5/6)^N
Now, the Limit of (5/6)^N as N tends to infinity is 1, but the value itself is never actually 1 for any finite value of N. As such, there is a slim chance that even if you rolled billions of dice you might not roll a single 6. A very small chance, but a chance anyway.
For the specific situation you mentioned, the probability boils down to:
P(winning the big prize if playing for N months) = 1 - ((1-1/1.2E6))^N
So if N = 1200000 then we have:
P = 63%
So, playing for 100000 years only gets you a 63% chance of winning the jackpot if your figures are right!
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Statistically speaking I am certain to win a million once if I keep my £30k in there for 100000 years.
Nope - You are never certain to win a million or in fact any prize.
Each draw is independent so you have the same chance of winning in each draw - it makes no difference if you haven't won anything in the previous 100000 years.
To calculate probabilities in this sort of scenario multiply the probabilities of not winning and subtract from 1 - obviously this can never result in 1 (certainty). It becomes increasingly les likely to not win as you consider more draws - but the probability for the next draw doesn't change.
Problem is that even if you were alive to reclaim the stake in 50000 years, it would be pretty worthless by then! Money devalues as time goes on, which is one of the main reasons why premium bonds can be a bad deal unless you win more often than average!
There is a slight problem with how the expected winnings (in the pink bars) appear on the chart. For instance if you select £5000 for 10 years and then compare with National Savings own "official Premium Bond rate" [PBR] you should win £1900 - and that can be seen immediately because the PBR is 3.8% and the winnings are assumed to be paid out so the 'interest' is 'simple' not compound.
However the dotted line drawn of the chart purports to be £1900 along the x-axis (somewhere between the marker at '£1000' and '£2500' ) I agree that it is positioned correctly but it lies slap bang in the middle of a thick bar. The bars represent cumulative probability so that they are only strictly the correct height on their left side - on their right side they 'jump' to the correct height.
I think this is only a minor quibble however, and I commend this site for offering it and explaining how it will be updated frequently - since NS&I does have a nasty habit of shaking the prize distributions around a lot when , say, it is simply moving the 'interest rate' by 0.2%. Thus a checker is a good idea.
Perhaps, therefore, MSE might consider a 'previous rates/prize distribution' option as time passes - just as you have 'current' and 'previous' interest rates often available on banks' sites etc? This would only entail doubling the size of the storage database (and memory is cheap) but no additional calculations (since the old database already contains these)
The results of the survey weren't "shocking". They were just as anyone with a a GCSE in Maths would have expected.
No-one here expects the government to give them something for nothing, do they?
If you are a higher rate taxpayer with a significant portfolio of savings and investments there could be a case for holding premium bonds, but surely not otherwise.
What's new?
Last edited by baby_boomer; 24-07-2007 at 9:52 AM..
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I read this piece in the Sunday Times with interest. I have no doubt that the clever maths may well be needed to create the database you have outlined but I think there is a far simpler method which requires only the distribution probability of winning a prize for a given stake and the actual average prize awarded - both obtainable from Ernie. Calculating the expectation value is then very straightforward.
Take my own case: I have a £30k stake which should yield 1.15 prizes a month. My own average prize over the last couple of years has been £60 which therefore gives 1.15*60*12= 828 for the year - or 4.6% equivalent for higher rate tax payer. In practice my prize rate has been 1.25 and that brings the higher rate equivalent up to 5%.
Actually its precisely because you took a £30k stake that it was relatively easy to work out. The less you take the more the various prize distributions layout impacts your odds. The more you put in, the nearly your payout is likely to approximate the interest rate.
Let's take someone who puts £1,000 in. Their odds are as follows
What are the chances? Winnings Probability
£0 Exactly
60.8%
At least £50
39.2%
At least £100
12%
At least £200
1.42%
At least £350
1 in 106
At least £500
1 in 106
At least £750
1 in 376
At least £1,000
1 in 376
At least £1,500
1 in 2,572
At least £2,500
1 in 2,696
At least £5,000
1 in 2,696
At least £10,000
1 in 5,859
At least £25,000
1 in 14,151
At least £50,000
1 in 32,607
At least £100,000
1 in 93,742
At least £1,000,000
1 in 1,500,000
A simple estimate would say at an interest rate of 3.8%, you're likely to win £38. Yet of course, that's in many ways a nonesense phrase as its impossible. You may therefore say well the nearest prize by far is £50, so i'm probably likely to get that. Though as the table above shows this is substantially less likely than winning nothing.
Quote:
A simple spreadsheet is all you need to work out what you might get and when from just simple parameters.
A simple spread sheet can give you a rough approximation of chances of winning in one or two draws. Then again - a spread sheet to compare how your £4,300 in premium bonds over a year compares to a savings account wouldn't be that simple! Plus this is a totally free tool open for anyone to use? So why would you bother creating a spreadsheet, to give you a rough, time consuming difficult answer when you can do it here, for free, with accuracy?
The results are surpising.
The black and white probability is surprising if you look through it. Have you read the article. Obviously many of you above are mathematically sophisticated. Lets remember a couple of facts.
A. Over 40% of people in the UK hold premium bonds
B. It is by many times the biggest single savings product
C. Most people don't understand how it works.
D. To provide information as to the realistic odds is crucial to help people make a rational decision which is exactly what this site is about.
I've done a lot of testing on this. And the results are shocking.
For example, many people who put £1,000 in and win nothing, consider themselves "unlucky". Yet actually the calculator shows they're nothing of the sort, in fact they have average luck as 60% of people who have £1000 in won't win anything over a year.
This tool goes a long way to dispelling the myths and making it easy for people to see what the odds are before making a decision. I'm very suprised at some of the rather, "I dont need it" attitudes above. However of course, if you want a refund for every penny you paid to use it, I'm happy to offer that
Quote:
Originally Posted by Milarky
There is a slight problem with how the expected winnings (in the pink bars) appear on the chart. For instance if you select £5000 for 10 years and then compare with National Savings own "official Premium Bond rate" [PBR] you should win £1900 - and that can be seen immediately because the PBR is 3.8% and the winnings are assumed to be paid out so the 'interest' is 'simple' not compound.
However the dotted line drawn of the chart purports to be £1900 along the x-axis (somewhere between the marker at '£1000' and '£2500' ) I agree that it is positioned correctly but it lies slap bang in the middle of a thick bar. The bars represent cumulative probability so that they are only strictly the correct height on their left side - on their right side they 'jump' to the correct height.
Thanks for this note and you are quite right. Unfortunately mapping the probability outlay any more accurately causes some massive database issues. Originally I didnt put the line on the graph, but then some people said they wanted a visible display.
To get the line on the graph - you need to click the compare box first, and the test explains accurately the odds. The box above is just to give an indicative visual representaion of how it works.
As for historic data, yes we're discussing how we can do that
Martin
Martin Lewis, Money Saving Expert.
Please note, answers don't constitute financial advice, it is based on generalised journalistic research. Always ensure any decision is made with regards to your own individual circumstance.
Sorry Martin but these results are not shocking. It really is not necessary for your model to be so complex simple maths can provide a sensible view of the likely outcomes.
I suspect that the choice of language to express what actually happens here is what is misleading.
I also suggest that most folks do have an at least intuitive understanding of what premium bonds can and can't do for them - ranging from the smaller punters for whom this is a low cost 'got to be in it to win it' bet - to the folks with the full £30k for whom it is a modest investment with the added bonus of a chance of hitting the big time - and the complete spectrum between.
I believe most folks do understand this - ie they are betting.
In other words most folks would forgo some of a low certain return for the outside chance of hitting the big time - exactly as they do in the lottery. For more on why this occurs see the recent article in the Economist on why people do behave in this way.
Last edited by The Bleurk; 24-07-2007 at 1:06 PM..
In any event it seems like a good bet to me given that I get my stake back whenever I want.
You DO NOT get your stake back. That is just a myth that NS&I like people to believe.
IF you got your stake back, it wouldn't be a stake. You only stake the nominal interest that your 'investment' has earned.
You could put £30K in a savings account and gamble the interest (about £1,500 per year). If you lost the £1,500 it wouldn't matter as you could still get your stake back - I think not.
Any chance of a similar calculator for The Lottery, so we can have a side by side comparison of
(1) Premium bonds and
(2) Putting money in a savings account and spending the interest on lottery tickets and/or scratchcards?
Quote:
We are the state's representative in our constituencies and we should not be frightened of taking decisions on behalf of our constituents, because that is to the general good.
The Rt Hon.Kevin Barron MP getting his job description a$$$ about t!!
£30,000 left in an Sainsbury internet saver @ 6.25% will generate £1,500 every year on interest, placing that on the national lottery will give you a 9,322/1 Chance of winning the UK jackpot in a year. (1,554/1 for 5 and the bonus and 1,332/1 for Jackpot or 5 and the bonus). the reason I chose these prizes because they are larger respectable prizes, the £1,500 you invest on the lottery could be sometimes the 5 balls prize.
Alternatively you could go to your local bookie and play the 49's Game which has a £150,000 payout for pick 5 match 5 which gives odds of 317,813/1 to win. your £1,500 interest from sainsburys account invested in this game gives you a 211/1 chance of getting the £150,000 Jackpot.
Pls be nice to all MoneySavers. There's no such thing as a stupid question, and even if you disagree courtesy helps. Take care over copyright. Use excerpts and links rather than copying long text. This site asserts copyright on all comments posted on the board.
Pls be nice to all MoneySavers. There's no such thing as a stupid question, and even if you disagree courtesy helps.
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