Wednesday, 7 December 2011

Savings Rate and Early Retirement (warning: some equations follow)

Yesterday I mentioned Jacob's blog at I'm going to look at his idea that saving ~75% of your income will let you retire in 5 years.

I'm sure the mathematics are in there somewhere, but the only figure I recall is that his assumptions are based upon a 4% draw down rate. I'm not sure exactly what this means. I'm currently reading up on investment so may understand better in the future. My "plain English" interpretation is that it means that you withdraw 4% of your capital each year to live off. Obviously there must be more to it than this, as either your income diminishes year upon year (4% of £200,000 gives you £8,000 in the first year, leaving you with only 4% of £192,000 = £7,680 in your second year of retirement), or you plan to die after 25 years of retirement having had an £8,000 annual income (not a great prospect if you retire at 35). Clearly he must have assumed some above inflation growth in the retirement fund.

Last night I did some calculations, using the assumption that your retirement pot keeps up with inflation (more on inflation later). To keep things simple I tried to keep the variables to a minimum (I assumed no savings, assets or debts at the starting point) , but there are many factors involved so it does get a bit untidy.

On the income side:

I = your net income. This is your take home pay after all deductions.

On the expenses side:

W= your work expenses, e.g. commuting, work wear, socialising that you feel is necessary
L= your other living expenses

On the time side:

A = your current age
R = your planned retirement age
E = the age at which you expect to end your reitrement

Your total savings before you retire come to (I-W-L)(R-A). This is your net income, less all your expenses multiplied by the number of working years you have left.
Your expected expenses after retirement total L(E-R) . This is your living expenses multplied by the number of years you expect to live after retirement.

If you have guessed your lifespan perfectly you need the first amount to be at least equal to the second amount.

With a little algebraic manipulation we get L <= [(R-A) / (E-A)] (I-W)

So what does this tell us? Let's take the case of a 40 year old who spends 10% of his or her net income on work expenses, wants to retire at age 50 and expects to live to 80.

We get

L <=  0.25 x 0.9 x I
 or L <= 0.225 x I

So this tells us that this 40 year old needs to cut their living expenses to 0.225 = 22.5% of their net income. In other words, allowing for their work expenses, they need to save 67.5% of their net income.

Say they were on £20,000 net per annum, they would need to save £13,500 of it.

That's not as bad as it may seem. It's likely that a 40 year old would have some form of pension and savings and they would need to adapt this calculation to take this into account.

You may still think that it's ridiculous and the 40 year old would be doing well to save 25% of their net income per year. Well here's the alternative. Rearranging the earlier expression we get

I >= L[(E-A) / (R-A)] + W

For that same 40 year old with work expenses of 10%, i.e £2000, with living expenses of £13000 and currently saving the rest, the expression becomes

I >= £13000 x 4 + £2000

i.e. their net income would need to immediately jump to £54,000!

That would typically require your gross salary to increase overnight from £26,000 to £82,000.

Which of the two statements in bold is the most do-able for you?

Even if neither of these situations seems valid, it should be clear that reducing your living expenses is far more likely to allow you to retire early than increasing your income.


  1. Hi. Thanks for visiting The Single Saver and commenting! Love your site! One thing to take into account in your scenario outlined above is that the saved money should, in theory, be earning interest and increasing in value if invested well. Let's even say it is a bad year and you only earn 3%... if you withdraw 4% and earn 3% you will only be down 1%. If you make more than 4% you are actually ahead. So the initial "pot" of money can actually last a very long time.

  2. Thanks for the feedback Single Saver. I'd assumed the interets on the savings was matching inflation. The problem with the scenario you suggest is the investing well bit and obtaining returns in excess of inflation.

    If you are merely saving as opposed to investing, you'll be doing exceedingly well to find interest even close to matching inflation. (If anyone knows of any such accounts, please do tell).

    It seems that a major aid to retiring early is being a good investor, or at least knowing one that is trustworthy. This is something I am trying to learn about.

    I'm suspicious of monte carlo simulations of future retirement income based upon past worst case performance. We are in an unprecented financial situation at the moment. Who knows what the outcome will be?