Beth's Exciting Asthmatic Adventures

About three months ago I got a bloody awful cold. Over the following weeks this was followed by a cough, then a sinus infection, then a chest infection. The chest infection then apparently triggered some kind of latent propensity for asthma that I didn't know that I had. Fundamentally I've just spent a lot of the last three months coughing, wheezing and feeling like I've been hit by a truck, leaving me with the attention span of a labrador and all the energy of a damp flannel.

A couple of weeks ago I went to the GP and mentioned that I was still exhausted, still coughing a lot, and still struggling to catch my breath. He got me to blow into one of these things:

Photograph of a peak flow meter

This neat little thing measures how quickly you can blow out air. It's called a "peak flow meter". I managed 230 L/min, which is around half the ideal peak flow for a woman my height and age.

As an aside, my first reaction on seeing this was to feel surprisingly offended - I hadn't realised just how much pride I took in my lung capacity, which is probably an attitude I picked up in wind orchestras over the years... However it was reassuring that I really did have some trouble with my lungs, and I wasn't just being an enormous wuss, even though being a wuss is usually a core part of my personality.

He gave me a peak flow meter of my very own and asked me to take a note of the recordings for a couple of weeks, and start taking a steroid inhaler after a couple of days.

This almost made the whole asthma thing worth it (as a computational biologist, data is a precious commodity). So merrily I began to record my readings and put them together.

The peak flow is on the Y axis, and the X axis is the date and time (each tick mark is the beginning of the day in question). The error bars are the standard error of mean for five readings at a time. As you can see, the readings are way above the 230 L/min I managed in the GP's office. I'm assuming that was a particularly bad afternoon because I'd been walking in the cold air. A healthy woman my size and age should have a reading somewhere in the range of 440-485 L/min, which I've been getting to on some evenings (yay!).

Looking at this graph I can see... a whole lot of nothing. This is chaos. What information could I get out of this?

Well, according to the GP, one of the classic signs of asthma is having a higher peak flow in the evening than in the morning. So let's take just the first and last reading from each day and plot them out. Here, the last reading is in blue and the first reading is in red.Graph of first and last peak flow measurements of the day

The morning readings are usually much lower than the evening readings, so that seems pretty cut and dried. I've put a little star over the days where the difference was statistically significant (p < 0.05, because as we know, 0.05 is a magic number).

The GP gave me two inhalers: one brown steroid "preventer" inhaler, which stops the lungs from getting inflamed, and one blue ventolin "reliever" inhaler, which stops the airways from spasming. Another classic sign of asthma is the readings improving after taking the blue ventolin inhaler. The data that's needed to work this out is a reading right before taking the ventolin, and one reading a sensible amount of time afterwards (half an hour seems about right). I only really gave this any thought today, so I'll have to collect more data in order to make any inferences. I know that my lungs subjectively feel a lot easier after taking ventolin.

These facts taken together make it sound pretty conclusively like asthma. It feels good to have a fairly definite diagnosis, because at least we know how to go about treating it.

The readings seem to generally be improving over time but there's so much variation that it's difficult to see a strong trend. The readings don't quite match up with how I've been feeling, either. Since Monday 16th I've been particularly wheezy and exhausted and on Wednesday 18th I honestly thought I might be dying, but the results don't make a noticeable downward swing. That said, I always do feel better in the evenings than in the morning, so that matches. I'm assuming I felt so much worse on Monday because of that big ol' dust cloud, because I can't think of another trigger.

I took two puffs from the blue inhaler at once one day last week and WOW was that horrible. Ventolin, it turns out, acts much like adrenaline in the body, leading to a racing heart and hands so shaky I couldn't even hold a restorative cup of tea. I briefly considered taking a beta-blocker to combat the side-effects but I feel as though taking a drug and then immediately taking the opposite drug is probably a bad idea? A little like swallowing a spider to catch a fly. Anyway, I won't be doing that again.

Other random thoughts:

  • The GP gave me a "spacer", which is a clear tube to put between my mouth and the inhaler, but I can't stop referring to it as "the bong" which does not make me sound as though I'm taking this whole thing seriously.
  • This asthma is likely to get better once the steroid inhaler does its job so I can't reasonably describe myself as chronically ill, but the Spoon Theory of dealing with reduced energy levels has helped a lot with prioritising tasks.
  • In that vein, I've been concentrating on doing the urgent and/or important tasks when I have the capability. Something that helps with this is a spreadsheet I made which is called "how long until things happen" and automatically calculates the number of weeks and days until various events. You can make a copy of this one and use it for yourself.
  • I'm surprised at how much I've missed exercising. I usually walk for about an hour every week day and do a fair amount of rowing and yoga on top of that. I joined an all-female powerlifting club before I got ill and I'd really like to get back to that as well. I last went to the gym about 2 months ago and I've been taking the bus to work when I'm capable of going in because the walk is absolute death. I have done a small amount of yoga when I've had the energy which is helping with all the odd aches and pains I get when I have several inactive days in a row.
  • Considering that I've basically been ill near-continuously for over 3 months, I'm surprised at how much I've gotten done. Heck yeah.
  • That said, I'm glad I have 4 different sets of pyjamas because I've spent a spectacular amount of time wearing them lately.
  • I treated myself to this pair of slippers a while ago and they are so warm and fuzzy, definitely worth the money. I got this blanket for Christmas and it has also been a great comfort.
  • I gathered as many pillows as I could find and made myself what I'm going to call my Pillow Throne in bed so that I can sleep propped up, which helps with the breathing at night.

So in conclusion, my Asthma Wisdom is:

  • Wear comfy pyjamas
  • Don't take two puffs of ventolin at once
  • Prioritise tasks as necessary
  • Make yourself a pillow throne

Asthmatic pals, do comment below with any of your top tips.

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Latte millionaire follow-up: no, millennials don't spend more on coffee.

A cup of coffee
image source

Last week, while procrastinating from writing my thesis, I put up a short blog post about a common piece of financial advice, viz: "if you avoid buying your daily latte and instead put the money in a savings account, you could be a millionaire by the time you retire."

I was surprised by the response that it generated - a Reddit post brought in 20,000 views to the blog, then it was picked up by the New York Post, which, bizarrely, I found out about from an automated message on LinkedIn titled "You made the news!".

The post didn't contain any information that wasn't already widely available - the formula for compound interest with regular deposits is a standard that can be found in any finance textbook. I re-derived it as an interesting afternoon exercise. I was surprised by just how many people picked up on the £318,135.57 figure rather than using the formula to calculate something based on their own costs and interest rates, or even just looking at the graph.

There have been a few comments that have come up more than once, so I thought I'd make a post addressing them.

What point are you trying to make?

Not much of one, really. The cost of a latte every day won't get you to a million before you retire at realistic interest rates, but it would save you a fair amount of money if you were prepared to give it up. People have interpreted the post in diametrically opposed ways, either: "you can save lots of money and should do this", or "don't deny yourself the pleasures of life". Pick whichever one you prefer - it's your life, not mine. Do remember to bring your own cup, though - we've only got one planet.

There is a persistent belief that people earning minimum wage could also be millionaires, if only they wouldn't spend so much on luxuries. I think this idea comes from taking the ideas from books like The Millionaire Next Door, about the frugality of the rich, to strange extremes. According to the Household Spending Survey from the Office for National statistics, people with the lowest 10% of income spend an average of £1.04 per day on eating out and going on holidays (far less, incidentally, as a percentage of their income than any other income group). Getting rid of this spending would save £378.82 over the course of a year, and get you to millionairedom with an interest rate of 6% in just 87 short years. If you wanted to be a millionaire within 50 years with a 6% savings account, you'd need to cut almost £10 a day from your budget, and the data show that people on low incomes just aren't spending that much on non-essentials.

It's important to be realistic about the limits of frugality, and not to use faulty mathematical reasoning when making financial decisions.

Where the hell are you finding an interest rate of 6%?

The last time I switched savings accounts was pre-Brexit - things are looking a lot worse for interest rates these days! I go to MoneySavingExpert for financial advice, and the best regular saver seems to get you around 5% back, but the majority of ISAs are at more like 1.4%. Please adjust your calculations accordingly.

What about taxes, investing, and 401Ks?

Firstly, we don't have 401Ks in the UK, we have other pension arrangements, so I can't tell you a darned thing about those. I can't tell you anything about taxes or savings accounts in the USA either.

As far as taxes in the UK go, I reckon you're going to be under the PSA allowance or the ISA allowance each year, so presumably that shouldn't be a big problem, but do correct me in the comments if I've misunderstood.

I've gotten lots of comments along the lines of "if you use my stock market strategy, you can get 15% returns!" I have no idea what the best investment strategy for your money is. Feel free to adjust your calculations to whatever interest rate you think you can find.

Millennials spend too much on coffee!

According to that same Household Spending Survey from the Office for National Statistics, the under-30s in the UK spend less on coffee and eating out than older people of working age. There was a widely-shared tidbit that millennials spent more on coffee than on their retirement savings, but this was based on a small SurveyMonkey form and certainly isn't held up by the ONS data, or US consumer spending data.

If my latte costs £x and my interest rate is y%, and I save for n years, how much money would I save?

I put together a calculator. Assuming you put your latte money into your account as a lump sum at the end of the year:

Latte cost (£): Interest rate (% AER): Years:

You would save £____.

What if I only get a latte on work days, not every day?

Well, let's assume that you work 5 days a week, and get 28 days of holiday a year. The number of days you spend working in an average year will be:

( 365.25 \times \frac{5}{7} ) - 28 = 232.89

Therefore our equation for yearly deposits becomes:

T_n = \frac{232.89 x (1 - y^n)}{1 - y}

In the £3 latte, 6% interest, 50 years example from the post, if you only have a workday latte to forgo, you'd save £202,848.99

What if I deposit the money daily rather than as a lump sum at the end of the year?

There's been a lot of confusion in the comments between yearly and daily compounding interest.

The interest rate % you are shown when you apply for a bank account is the "annual equivalent rate" (AER). The AER tells you how much interest you would get if you put a lump sum in at the beginning of the year and then didn't add anything else.

In reality, most bank accounts work out your interest daily, and then pay it in at the end of the year. A yearly interest rate (AER) of y applied to an initial deposit of £x should get you the same amount of money at the end of the year as a daily interest rate of z applied every day, i.e. 365.25 times. Therefore, using the classic formula for compound interest (T_n = x y^n ):

x y^1 = x z^{365.25}

Rearrange to get z in terms of y:

z = y^{\frac{1}{365.25}}

The equation we used for yearly compounding interest becomes:

T_n = \frac{x (1 - z^{365.25 n})}{1 - z}

Where T_n is the total money you have at the end, x is the cost of your latte, z is your daily interest rate that we calculated above, and n is the number of years that you want to save for.

You'd make extra money saving every day rather than at the end of the year. In the example I used in my original post, with a £3 latte at 6% interest for 50 years, you'd make £327,560.82 rather than £318,135.57, a not inconsiderable difference of £9,425.25 (although still notably not a million).

The daily model of saving is probably a more realistic one than my original, yearly lump sum model, so let's make a calculator for that, too:

Latte cost (£): Interest rate (% AER): Years:

You would save £____.

If you want to work out accurate daily interest calculations for lattes bought only on work days, you're on your own unless you feel like sending me your holiday schedules for the next 50 years. As a rough estimate, you could multiply your latte cost by \frac{232.89}{365.25} and use the above calculator.

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The latte millionaire fallacy

Edit: This got picked up by the New York Post - hi to everybody who clicked through from there.

coffee-922914_640

An idea oft floated around the internet is: "if you avoid buying your daily latte and instead put the money in a savings account, you could be a millionaire by the time you retire." I think it was the book "The Automatic Millionaire" by David Bach that first popularised the idea.

I'm not going to argue that it's not worth saving money on non-essentials (although if you're in dire financial straits you probably don't need to be told this - contrary to some oddly popular rhetoric, people with low incomes do tend to also spend less money, especially if they are unemployed).

What bothers me is that, at realistic interest rates, you're very unlikely to make it to a million pounds. You'd save a lot of money, but you'd be far short.

Other people have also written about this, but I thought I'd quickly break down the maths.

Say you spend x pounds on a latte every day (in reality, probably around £3). Instead of buying this latte, you decide to invest the money in a savings account with an interest rate of y (probably between 3-6%). After n years, you will have £T.

So how do we work this out?

At the end of the first year, you put in £x.

T_1 = 365.25 x

In the second year, you'll get the first amount with interest, plus all the money you've added in the second year.

(Sidenote: I'm using a multiple for the interest, e.g. 3% interest is expressed as 1.03)

T_2 = 365.25 x y + 365.25 x

The next year, you get all of that money with interest, plus your new deposits.

T_3 = (365.25 x y + 365.25 x) y + 365.25 x

This could also be expressed as:

T_3 = 365.25 x y^2 + 365.25 x y + 365.25 x

This is looking like a geometric series, yay! If we come up with a generic expression for the total amount, it looks like this:

T_n = 365.25 x y^{n-1} + 365.25 x y^{n-2} + ... + 365.25 x y + 365.25 x

Now, if you can remember your GCSE maths, the way we find out the sum of a geometric series is by multiplying it by y:

T_n y = 365.25 x y^{n} + 365.25 x y^{n-1} + ... + 365.25 x y^2 + 365.25 x y

and then taking it away so you can cancel out most of the terms:

T_n - T_n y = 365.25 x - 365.25 x y^n

Now let's get all the T_ns on one side of the equation, and everything else on the other side:

T_n (1 - y) = 365.25 x (1 - y^n)

T_n = \frac{365.25 x (1 - y^n)}{1 - y}

So if you invest your £3 per day latte money into an account paying 6% interest for 50 years, you'll end up with:

T_{50} = \frac {365.25 \times 3 (1 - 1.06^{50})}{1 - 1.06}

T_{50} = \pounds 318,135.57

Don't get me wrong, £318,135.57 is not chump change, but it's less than a third of the way to a million.

In fact, if you wanted a million pounds from a £3 latte habit, you'd need an interest rate of 9.6%. At an interest rate of 6%, your latte would have to cost £9.43.

Here are all the likely interest rates and latte cost combinations that will net you a million pounds by this method:

Minimum interest and cost combination required to accumulate a million pounds
Interest rate - latte cost combinations required for millionaire-dom

As you can see, you'd require a very high interest rate or a very expensive latte.

Again, I'm not against saving money and making your coffee at home; I'm against the propagation of inaccurate mathematics.

XKCD cartoon about compound interest
As always, XKCD said it best.

Addenda:

  1. I was thinking about inflation, but decided that there were too many factors to consider (your money would be worth less at the end, but also your latte would cost more and perhaps your interest rate would rise...)
  2. Several people have mentioned that it's likely that people would only buy their latte on the way to work for 5 days a week. They'd also have some holiday days during the year. Considering how much shift work, zero-hours contracts, overtime, and working multiple jobs that people do, calculating these factors made my head hurt, so I choose instead to believe that these people go out on the weekends for a latte at the nice artisan café down the road.
  3. It has also been pointed out that finding a bank account with a 6% rate of interest is nigh-on impossible. If I've interpreted the maths correctly, this means that you won't become a millionaire unless you start buying a more expensive latte.

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