Posts Tagged ‘graph’

2012 – 2013 UK tax graphs for income tax and NI

Wednesday, April 18th, 2012

I’ve been publishing UK tax graphs since the 2008-2009 tax year. It is easy to find tax information in the official government tables, but it is very hard to find simple graphs that show that the numbers mean in simple terms which is why I make these graphs. I missed out last years graphs so this year I will include the 2011-2012 and the 2012-2013 tax years. The 2010-2011 tax year is also included for comparison.

First of all here is an overview of the overall percentage of tax paid for salaries up to £200,000. The percentage for the 2011-2012 and 2012-2013 years jump mainly because of the national insurance rate increasing from 1% to 2% for earnings above the upper earnings limit.

percent tax vs gross salary 2012 2013 2

At the more average end of the salary scale the change between the years is more affected by the increase in the personal allowance.

percent tax vs gross salary 2012 2013 1

Here is a closer look at the income tax. It shows that the changes between these years have been fairly minor. There is always a lot of talk about tax changes in the budget, but in reality things don’t change much.

income tax 2012 2013 2

income tax 2012 2013 1

The national insurance graphs show a larger change for higher earners since the 2011-2012 tax year because of the 1% rate increase.

national insurance graph 2012 2013 2

national insurance graph 2012 2013 1

And finally two charts showing the absolute change in pounds paid as tax during these two tax years. These show that taxes for average earners have been decreasing, and taxes for higher earners have been increasing.

uk tax change 1011 1112

uk tax change 1112 1213

More next year…

2010-2011 UK Tax graphs

Tuesday, June 15th, 2010

Straight after putting up the tax graphs for 2009-2010, I’m putting up the tax graphs for this tax year. This time the graphs are better, and some of them include a comparison line with the previous year’s figures.

As before I’ll state I’m not an accountant or tax expert so I can’t guarantee their accuracy, but I’ve done my best. The graphs assume that you are getting the default allowances. Let’s start with an overview of how much tax you’ll pay.

2010 2011 total tax graph

The big change for this year is the new higher 50% rate of tax, and the tapering off of your personal allowance once you reach the income limit. For most people this has no impact, it is only once you start getting over £100,000 that your tax will rise. You can clearly see the change in tax by comparing the red and blue lines in the graph.

Next is a more visual way of seeing the tax changes. The first slope is where the personal allowance tapers off, and the next one is where the 50% tax band kicks in.

2010 2011 tax changes

Income tax and national insurance

The overall tax you’ll pay is composed of income tax and national insurance. Here are two graphs showing how much of each one you’ll be paying.

2010 2011 income tax graph

2010 2011 national insurance graph

Gross salary vs net salary

Here is a graph showing your gross salary vs your net salary.

2010 2011 gross salary vs net salary graph

And a more zoomed in version which only goes up to £60,000.

2010 2011 gross salary vs net salary graph zoomed

Percentage of tax

And finally I have a graph showing the percentage of tax you pay against your gross salary. You can see that the new tax changes have made the shape more uneven (i.e. more complicated) than in the previous tax year. This is sure to be good news for accountants!

2010 2011 tax vs gross salary

2009 – 2010 UK tax graphs

Thursday, June 10th, 2010

Here are some graphs showing income tax, national insurance, total tax and percentage of tax for the 2009-2010 tax year. I have also included a graph showing how total taxation has changed from the 2008-2009 tax year. If you want tax graphs for the current tax year go to my 2010-2011 tax graphs page.

I’ve done my best to make these accurate; however I’m not a tax expert so I can’t guarantee these are correct. These are therefore just for interest, and not for serious use.

2009-2010 income tax

First up income tax – everyone’s favourite tax!

2009 2010 uk income tax graph

After a short tax free allowance you can see how the basic rate of tax hits, and then the higher rate of tax causes the angle to increase.

2009-2010 national insurance

National insurance follows a different shape as once you reach the higher band the rate drops to 1% rather than increasing.

2009 2010 uk national insurance graph

2009-2010 total tax

This graph combines both the income tax, and national insurance to show the total amount of these taxes that you would be paying.

2009 2010 total tax graph

And here is a version that is more zoomed in – it only goes up to £60,000.

2009 2010 total tax graph zoomed

2009-2010 percentage of tax

Perhaps more interesting than the amount of tax you pay, is the percentage of tax you pay. This graph shows the combined income, and national insurances taxes against gross salary. The dip somewhere after the £40,000 level is due to the national insurance dropping to the 1% rate before the higher rate of income tax kicks in.

2009 2010 uk percentage of gross salary as tax graph

Change in tax from 2008/09 to 2009/10

This final graph shows how the amount of tax you pay has changed from the previous tax year, to the 2009/10 tax year. You can see that the amount of tax to be paid has actually decreased. This is due to the increase in personal allowance for 2009-2010.

0809 0910 tax change graph

Visualising the Google PageRank scale

Friday, April 9th, 2010

Google’s PageRank is a scale from 0-10 that shows how well connected web pages are. Web pages with higher PageRank values have more quality links pointing to them. It is not a linear scale, it is a logarithmic scale.

People estimates that the logarithm base is between 5 and 10. Because it is a logarithmic scale it can be quite hard to visualise.

I’m going to try to visualise PageRank with some graphs. In these graphs I’m making the assumption that the log base is 5. The first graph shows the values from 0-10 on a linear scale.

pagerank 1 to 10 on log base 5

You can see that when the logarithmic scale is converted into a linear scale the difference between most of the lower numbers completely disappears. That is why these things are presented on logarithmic scales! I’ve added a few websites onto the scale so you can see where they are.

As most websites aren’t in the 7-10 range I’ve produced another graph showing just the values 2-7. I’ve made the graph very tall so you can see the difference between the values better. Again I’ve added a few websites onto the graph so you can see what kind of websites get the upper PageRank values.

pagerank 2 to 7 on log base 5

The above two graphs are making the assumption that the base of our logarithm is 5. Would it make much of a difference if it was 10? Yes it would make a huge difference.

Here is a graph comparing what the PageRank linear values might be for a log base 10 graph vs a log base 5.

log base 5 vs log base 10

You can see that it is not practical to plot multiple logarithms on the same graph, so it would make a huge difference whether the logarithmic base was 5 or 10.

As for whether PageRank really matters – it probably counts for less than most people think. The toolbar PageRank of one of my sites recently went from 2, to 0, up to 3 and back down to 0 again. During these changes I noticed no change in traffic. The actual page contents and TrustRank probably counts for much more than PageRank on most web sites.

2008 – 2009 UK Tax Graphs

Monday, September 1st, 2008

I’ve produced some graphs using data about the 2008 – 2009 UK tax situation (I also have tax graphs for 09/10 and 10/11).

I’ve tried to make them accurate but beware that I’m not a tax expert so there could well be errors. They have been created for interest only, not for serious use.

The first graph is showing how much income tax you pay depending on how much you earn. This graph is based on the standard un-adjusted tax free allowance of £6305, a 20% band for the next £34800 and 40% after that.

income tax 08 09

Next is a similar graph but for national insurance contribution. I’ve used £105 per week as being free from NICs, 11% for £105-£770 per week and 1% after that.

national insurance 08 09

The third graph combines the total of the two to show the total taxation.

total tax 08 09

The final graph shows what percentage of your gross income you pay as tax. The interesting shape is caused by the National Insurance contributions changing to 1% before the 40% tax band kicks in.

percentage of income as tax 08 09

You may spot that when your salary reaches just over £40k the percentage of salary that you pay in tax actually goes down by a very small amount before going back up again.

Graphing the AXA Sun Life 50 Plus Protector

Wednesday, August 27th, 2008

Following on from my post where I graphed the AXA Sun Life Guaranteed Over 50 plan I thought I’d look at a more complex product to see what kind of graphs I could get out of it. Unlike the Over 50 plan, the AXA Sun Life 50 Plus Protector features a lump sum and premium that increases over time. There is also a maximum number of years that the premiums are payable for. As there are a number of extra rules it should produce some interesting graphs!

As before I’ll mention that I’m not writing this to offer an opinion on this particular product. I’m not a financial advisor. My interest is to show how you can convert the information about financial product into graphs. These graphs can be of great help in deciding whether a financial product is suitable for you.

I got a quote from their website for a 60 year old male paying in a premium of £7 per month. These figures are what I was quoted on the day I did the quote (late August 2008).

The premium of £7 will rise by £0.35 per year for a maximum of 20 years when it will be double the initial premium. It will then remain level until it stops altogether at the age of 90. The cash lump sum is payable on death after two years. It is £1095 and will rise by £50 per year. If you were to die within two years the lump sum would be 1.5x the amount paid into the plan. There is no cash in value – if you stop paying money into the plan you get nothing.

The first graph I’ll make is to show how your premiums vary over the years. You can see them increasing every year, until the age of 80 when they level off. After the age of 90 you don’t pay any more premiums.

axa sun life 50 plus protector cost of premium

The next graph shows the cumulative cost of all the premiums paid into the plan, against the value of the lump sum. You can see (if you look carefully) that the premiums paid line increases in angle for the first 20 years. It is then a straight line for the next 10 years. The line then goes flat from age 90 as no more premiums are payable. The lump sum payment starts off at 1.5x the amount of premiums paid in, after two years it goes to the full lump sum value which increases by £50 each year.

axa sun life 50 plus protector plan cost vs lump sum

You can see that there is a crossover point at which you pay more in premiums than the lump sum you get back. You can also see that as you don’t pay any more premiums after age 90 the lines start coming together again. I continued the age range to 120 to see at what point they diverge for the second time.

I then produced a graph to show by what percentage the lump sum and the premiums go up. The text on their website says that both go up by 5% of the original lump sum / premium each year. An increase of £0.35 is indeed 5% of the £7 premium. However £50 of £1095 is actually 4.6%. I’m not sure whether they are rounding the lump sum increase down, or whether there is some error in their calculation.

axa sun life 50 plus protector lump sum increase

Despite the slight discrepancy in percentages both premium and lump sum follow an almost identical curve of decreasing percentage increases each year. The premium increases drop to 0% after the age of 80 as per the plan description. The lump sum increases by £50 each year so the percentage increase keeps dropping. It is therefore important to understand the effect that inflation will have on this plan.

I hope you found this interesting. These three graphs took me about 15 minutes to do and provide details of this product in a much easier to analyse format than the pure text description of the product as given on the AXA page.

As I started before I’m not offering you an opinion of their plan, more a reason why getting to grips with a spreadsheet package like Microsoft Excel will help you with making financial decision.

Graphing the AXA Sun Life Guaranteed Over 50 Plan

Friday, August 22nd, 2008

On TV recently I’ve been bombarded by adverts about the AXA Sun Life Guaranteed Over 50 Plan. The current version of the advert is presented by Michael Parkinson. Previous versions have been presented by June Whitfield.

I am no way near the age of 50 and these plans have no relevance to me. I should also point out that I am not a financial advisor, and am not intending to offer any opinion on these plans. My interest is to look at them from a simple mathematical point of view.

In case you’ve missed the advert the basic idea is this. If you are over 50 you can pay AXA a fixed monthly sum for the rest of your life. When you die a fixed sum (fixed at the time you open the plan) is payable to your family. If you die within two years you don’t get the fixed sum, but your family do get 1.5x your premiums back. If you ever stop contributing you don’t get anything.

I went on their website and got a quote for a 60 year old male paying in £6 per month (the minimum a 60 year old male can pay in on the day I got the quote). This produces a cash lump sum of £760, payable on death after 2 years.

Here is a graph plotting how much you pay in, against how much you get back. You can see there is a cross-over point at which you end up paying in more money than you get back. In this case you end up having paid in more then you’d get out when you reach 71 years old.

axa sun life over 50 plan graph

The government publish data on life expectancy. I got the latest male life expectancy data from 2004 and 2006 and plotted this into another graph. Note how your life expectancy goes up as you get older. This is because you have already managed to avoid dying in the preceding years.

uk life expectancy

You might not be able to make out the detail on the graph but the life expectance for a 60 year old male in the UK is 80.81 years.

This means that if you are an average person you are likely to be paying in 9 years of premiums beyond the lump sum value that you would get back.

However calculating the benefit of these plans isn’t quite as simple as this – they often provide extra benefits such as extra payouts in the event of dying in an accident or whilst travelling.

An obvious factor to look into is the effects of compound interest when adding the same amount (£6) into a bank savings account every month.

compound interest graph on a monthly saving of £6 at 4%

This graph is showing the effect of saving £6 a month based on a modest 4% gross interest rate. I based the calculations to produce this graph on the formula given on patrick schneider blog post. The final figure after 40 years matches the figure given by other compound interest monthly savings calculators I’ve seen on the internet so hopefully the graph is accurate!

Below I’ve put the compound interest curve on top of the previous graph comparing contributions against the cash lump sum.

compound interest graph on a monthly saving of £6 at 4% compared against AXA Sun Life Plan with £6 per month contribution

There are further complications to consider such as the effect of inflation. The real worth of any money your family would get back when using these plans is reduced every year due to inflation. On the other hand the real world cost to you goes down each year as your £6 per month will gradually constitute a smaller percentage of your income.

What are my conclusions? I’m not giving you any! Any decision on whether to use a financial product should be taken based on your personal financial circumstances and with the help of a trained financial advisor (which I’m not).

I would say that these are the kind of analyses you should be doing when investigating or comparing any kind of financial product, whether it be a savings account, loan or mortgage. Turning financial information into simple graphs is a very powerful tool that can save you a lot of money!