Six maths lessons everyone can learn to get richer

Becky O’Connor of PensionBee explains personal finance maths in a way anyone can understand and use themselves

Becky O’Connor is director of public affairs at PensionBee.

 How would you rate your own financial literacy? Moreover, how important do you think it is to your financial wellbeing? 

Most experts agree that as a nation, we need more personal finance education.

There are some obvious and less obvious reasons. The need to budget and understand the cost of debt are clear reasons to brush up on basic spreadsheet skills and how to calculate percentages. 

But what about the maths lessons you don’t even know you might need, which could help you build wealth more effectively?

In not understanding the long-term benefits of a pension over, say, a savings account, millions of people could be missing out on much bigger retirement pots.

It is especially important that younger workers understand some of the maths behind pensions in particular, so that they grasp the benefits of saving as much as possible as early as possible and can take advantage of any opportunities they might have to get ahead, for example, double-matched employer contributions.

There’s a risk that if we don’t all take the time to understand things like compound growth, we’re less likely to proactively do something beneficial, like maximise employer pension contributions.

Here are six real life maths lessons that can make everyone richer when they get older.

1. Compound growth: Generates massive gains the longer you save and invest

The benefit of growth on top of growth over time is key to why people need to save into a pension as early as possible.

Compound growth means that the amount of interest, dividends or capital gains your savings or investments earn each year is calculated on top of the original amount, plus any interest, dividends or capital gains already accrued, amplifying the gain.

A simple example of compound growth might look like this – Investment £1,000, annual return, and total capital including growth at the end of each year

Year 1 – 5% £1,050

Year 2 – 5% (of £1,050) £1,102.50

Year 3 – 5% (of £1,102.50) £1,157.63

Year 30 – 5% (of £4,116.14) £4,321.94

Year 40 – 5% (of £6,704.25) £7,039.99 

This assumes 5 per cent investment growth, an 0.7 per cent fee, a £24,000 starting salary and a retirement age of 68.

So you can see that the more years you are investing for, the more chance your returns have to compound. This starts slowly but leads to massive gains over time, which is why it’s a good idea to start saving into a pension as soon as possible.

This is why financial experts keep saying that starting a pension in your 20s rather than your 30s will make a huge difference to your eventual pot. But don’t be discouraged if you start late, because you will still benefit from compound growth.

>> How much do YOU need for a decent retirement? 

2. Charges: Compounding works against you, too

It’s worth knowing the way compounding can work against you, too. 

Any pension or investment comes with a fee (which may be a newsflash in itself – Isas and pensions are not free services). 

Here’s what that might look like in practice, all else being equal. 

This assumes annual return of 5 per cent, initial investment of £1,000 and contributions of £100 a month.

3. Tax relief: A free boost to your pension

The main advantage of pensions over other forms of very long term saving is that whatever you put in, your ‘contribution’ attracts tax relief.

Put another way, if you take that bit of income now and keep it, you pay tax on it. If you put it in a pension, you do not.

This means you get an effective uplift on what is going into your pension compared to what that amount would be if you put it in a savings account or Isa after having already paid tax on it.

For every £100 you put in, the government usually adds another £25 under current tax rules.

To work out what your total contribution would be given a specific personal contribution figure, if you are a basic rate taxpayer, add 25 per cent to the amount you personally are putting in before tax relief is applied.

(The 20 per cent tax relief is 20 per cent of the total contribution including tax relief, not 20 per cent of what you initially put in – a common source of confusion).

If you are a higher rate taxpayer, add 67 per cent and if you are an additional rate taxpayer, add 82 per cent of the amount you are personally putting in, before tax relief.

At first glance, it looks a little unfair that higher rate taxpayers get more relief. But remember it just represents the higher tax that person would have paid had they taken their income now rather than deferring it via a pension.

They will have to pay income tax on that money in future, when they start to draw it as income. However it will most likely be a lower rate of tax (most pensioners either don’t pay tax or just pay basic rate tax).

> Read our guide: How pensions work – what you need to know

4. Inflation: Beat the decreasing value of money by investing

One reason it is important to invest over the very long term, rather than just put your money straight into a savings account, is the impact of inflation on the value of money over time.

If inflation is at 2 per cent for 10 years, the value of £10,000 now would be £8,203 in today’s money in 10 years’ time.

Pension investments aim to beat inflation over time, preserving and growing the value of your money. So if investment growth is 5 per cent and inflation is 2 per cent over a period, the net increase in value of the pension pot is 3 per cent.

Here are examples of pension pot values now, and what they could be worth in today’s money when someone retires if there is no investment growth and no further contributions and inflation is 2 per cent a year.

And here is the difference with net pension growth of 3 per cent (5 per cent investment growth a year, minus 2 per cent inflation)

This is why it is so important that pensions are invested to beat inflation. Without the long-term average annual growth that the stock market has historically delivered and is expected to deliver in future, your money could be eroded by inflation to the tune of something like the above.

5. Percentages: What is 8% of your salary in pounds?

It is important to understand how percentages work for managing finances in general.

With pensions specifically, knowing how to convert percentage values into pounds and vice versa is useful so you know how much you are contributing, how much tax relief you are getting, how much your employer contributions will add up to and how much your investment has grown by or is expected to grow by, among other things.

For example, to calculate 8 per cent (the minimum pension contribution under auto enrolment) of £35,000 (an example salary), simply divide £35,000 by 100 and multiply this number by 8. The answer is £2,800.

There are many percentage calculators online which will do the above sum for you.

Meanwhile, the table below is the breakdown of what makes up the 8 per cent contribution. Use your own salary and work out what percentage in pounds you, your employer and the Government (which pays you the tax relief) are making to your pension.

Who pays what: Auto enrolment breakdown of minimum pension contributions. (Qualifying earnings are those between £6,240 and £50,270 of salary)

6. Pound-cost averaging: The benefits of drip-feeding pension investments

Pound-cost averaging is the effect on your money of making small, regular contributions to reduce the impact of market ups and downs on the value of your investment over time.

Pound-cost averaging means there are benefits to continuing to invest even when the market is down, because when prices are low, the amount of money you invest can buy more units of a particular investment.

This means that when prices rise again, there is greater benefit to the investor, because they hold more units of that rising investment.

For example, if a £100 investment buys 10 units of a fund, at a cost of £10 each then the value goes up to £15 a unit a year later – great! Your investment is worth £150.

But say you want to invest another £100 at that price – your £100 would now only buy 6 units, because the value of each unit has risen.

But instead, let’s assume the value has gone down to £5 a unit. That’s annoying for the value of your previous £100 investment – it’s now worth £50. But that’s only troubling if you sell.

Let’s say you buy in again with another £100. That £100 now buys you 20 units rather than 10, at a value of £5 each. A year later, the value of each unit rises £20.

Amazing! Not only has your first set of 10 units recovered its losses to now be worth £200, your second set of 10, which you bought at the cheaper rate of £5 each, has gone up in value to £400.

For a total cost of £200, your investment two years later is worth £600. You are very glad you didn’t sell low, but instead bought more units and benefited from the eventual gain.

The great thing about making regular contributions to a pension – which is essentially just a stock market investment plan – is that you can benefit from this effect during stock market lows if you keep contributing.

> Long-term saving and investing calculator: See how your wealth can grow