Financial Education

The Maths Behind
Growing Wealthy

Understand why time — not just rate — is your most powerful financial tool. Plain English, real UK examples, interactive calculator.

✓ No jargon
✓ UK examples
✓ Interactive learning
🔒 No data stored
ℹ️ For educational purposes only — not financial advice. Examples use assumed rates to illustrate concepts. Your actual returns will vary.
1
Would you rather have £100 today or £100 in a year?

It sounds like a trick question. The amount is the same. So why does it matter when you get it?

Which would you choose?

✓ £100 today is the right answer — and most people's instinct. Here's why.
📈
You can invest it
£100 today, invested at 5%, becomes £105 by next year. The future £100 stays £100.
📉
Inflation erodes value
Prices rise over time. £100 in a year buys slightly less than £100 today.
⚠️
The future is uncertain
The promised £100 in a year might not arrive. Money in hand is certain.

These three reasons form the foundation of all personal finance. Together they explain why money paid sooner is always worth more than money paid later — and by how much depends on interest rates and inflation.

Economists call this the Time Value of Money. It explains every mortgage, every ISA, every pension — and every financial decision you'll ever make.

2
Interest — your money earning money

Interest is simply the price of using money. If you borrow it, you pay interest. If you save or invest it, you earn it.

At its simplest: put £1,000 in a savings account paying 4% per year. After one year, you earn £40. You now have £1,040.

📘 Example — Simple Interest
£1,000 × 4% × 1 year = £40 interest
Total after 1 year: £1,040

After 2 years: £1,000 × 4% × 2 = £80 interest → £1,080
After 5 years: £1,000 × 4% × 5 = £200 interest → £1,200

Simple interest grows in a straight line — the same £40 every year, because it's always calculated on the original £1,000 only.

But what if you left the £40 in the account instead of taking it out? Something more powerful starts to happen...

Show me the formula
Interest = Principal × Rate × Time
e.g. £1,000 × 0.04 × 1 = £40
3
Compound interest — the snowball effect

Let's switch to a 7% rate — closer to long-run stock market returns — to make the compounding effect clear.

In year two, you don't earn interest on just £1,000. You earn it on £1,070 — because the £70 you earned in year one stayed in the pot and started earning interest too.

Year 2: £1,070 × 7% = £74.90. Not £70. That extra £4.90 seems trivial. But watch what happens over time.

Year Your pot Growth this year 'Free money' from compounding
1£1,070£70£0
2£1,145£75£5
5£1,403£92£22
10£1,967£129£59
15£2,759£181£111
20£3,870£253£183

Based on £1,000 invested at 7% per year, no further contributions.

By year 20, your pot earns £253 that year — but £183 of that is 'free money' you didn't put in. It's your earlier interest now earning its own interest.

The snowball starts small and slow. But it gets bigger every year — and the bigger it gets, the faster it grows.

💡 Key Insight
In year 1, compounding adds £0 extra. By year 20, it adds £183 extra per year — on the same original £1,000. Same money. Same rate. Just time.
Show me the formula
Future Value = Principal × (1 + Rate)^Years
e.g. £1,000 × (1.07)^20 = £3,870
4
Try it with your own numbers

Enter a starting amount and a monthly contribution — or just one of them. See how compounding builds your pot over time, and find the moment when your pot earns more in a year than you put in.

View:
UK long-run avg ~2.5%
What you put in
—
Total contributions over the period
Your pot
—
Nominal value at end of period
Growth from compounding
—
The 'free money' — pot minus what you put in
🎯 The Crossover Point — Year —

By the end of Year , your pot has reached —. At % return, it earned — in growth that year — more than the — you contributed. The teal line on the chart marks this moment.

In plain English: before the crossover, you are doing most of the work — your monthly payments are bigger than what the pot earns. After the crossover, your pot takes over. The bigger it gets, the faster it grows — which is why the blue line steepens sharply in the chart's later years.

5
Inflation — the silent thief

There's something working against you at the same time. Silently. Every year, prices rise — and your money buys a little less.

This is inflation. At the UK long-run average of around 2.5% per year, £100 today will only have the buying power of £61 in 20 years' time.

Today —
£100
Buys a full basket of shopping, a tank of fuel, or a couple of meals out.
→
2.5%/yr
for 20 yrs
In 20 years —
£61
That same £100 note will only buy what £61 buys today. The note hasn't changed — but its purchasing power has shrunk.

What does this mean for your investments? If your ISA earns 7% and inflation runs at 2.5%, your real return — the actual increase in purchasing power — is only about 4.4%, not 7%.

📘 Nominal vs Real Return
Your ISA return: 7% (nominal)
Inflation: 2.5%
Real return: (1.07 ÷ 1.025) − 1 = ~4.4%

So your projected £104,000 ISA pot in 20 years is worth roughly £64,000 in today's money. Still excellent — but a truer picture.

This is why the calculator above has a "Real (today's money)" toggle. Switch to it and enter an inflation rate — you'll see the difference between what your pot says it's worth and what it can actually buy.

Inflation doesn't make investing pointless — it makes it more important. Leaving money in cash means it's almost certainly losing real value every year.

Show me the formula
Real Return = (1 + Nominal Rate) ÷ (1 + Inflation Rate) − 1
e.g. (1.07 ÷ 1.025) − 1 = 4.39%

Real Pot = Nominal Pot ÷ (1 + Inflation)^Years
e.g. £104,185 ÷ (1.025)^20 = £63,572
6
What this means for you

These concepts aren't academic. They explain three of the biggest financial decisions most UK households face.

💵
Cash Savings — the silent trap
Cash savings do compound — interest earns interest. But the rate is typically so low that inflation still wins over the long term. Even a competitive savings account often struggles to keep pace with rising prices, so in real terms your purchasing power quietly erodes. The longer the time horizon, the more this gap matters.
📈
Stocks & Shares ISA
£200/month invested for 20 years grows to a projected pot of £104,000 — based on an assumed 7% annual return (a commonly used long-run estimate for a diversified equity portfolio, not a guarantee). You put in £48,000. The other £56,000 came from compounding — and most of it arrived in the final 4 years. Factor in inflation and the pot is worth less in today's money — but the compounding effect remains just as powerful. Actual returns will vary and capital is at risk.
🏠
Mortgage Overpayment
Overpaying your mortgage is compounding working in reverse — every £1 off the balance means less interest charged next month, and the month after. The saving is guaranteed and risk-free at your mortgage rate.

Overpaying £1 early saves more interest than overpaying £1 late — because early payments remove principal that would have kept compounding against you.

Always check for Early Repayment Charges (ERCs) first — your lender may limit how much you can overpay penalty-free each year.
🏦
Pension
Starting a pension at 25 vs 35 — same contributions — can result in a significantly larger pot at retirement. The extra 10 years of compounding does more than an extra 10 years of contributions could. Factor in inflation and both pots are worth less in today's money — but the gap between starting early and starting late remains just as stark. Time really is the most powerful input.
✓
5 things to remember
01
Start early — time does more work than rate
10 extra years of compounding beats a higher return almost every time.
02
Compounding accelerates in the final years
The last 4 years of a 20-year ISA generate nearly 4× more growth than the first 8 years combined.
03
Inflation is always running — think in real terms
A 7% return isn't really 7% after inflation. The real number is what matters.
04
A guaranteed return vs an uncertain one
Paying off your mortgage saves interest at a guaranteed rate. Investing targets a higher return — but it's not certain.
05
The crossover moment is the goal
When your pot earns more each year than you put in, your money is working harder than you are. That's financial freedom starting.

Now put it into practice

You understand compounding and the time value of money. See how it plays out in one of the most common UK financial decisions — overpaying your mortgage vs investing in a Stocks & Shares ISA.

Open the Mortgage vs ISA Calculator →

Common questions

What is the time value of money?+
The time value of money is the principle that money available now is worth more than the same amount in the future — because it can be invested to earn a return, and inflation erodes purchasing power over time. It underpins every interest rate, mortgage calculation, and investment decision.
Does cash in a savings account compound?+
Yes — cash savings do compound. Interest is added to your balance and then earns interest itself. The problem is that savings rates are typically low enough that inflation still erodes your purchasing power over time. Compounding works in your favour with cash, but often not fast enough to keep up with rising prices over a long horizon.
When does compounding really start to make a difference?+
Compounding is always working, but its impact accelerates over time. The gains in the later years of an investment period can dwarf those of the early years — on exactly the same monthly contribution. There's a crossover point when your pot's annual growth exceeds what you're putting in each year: from that moment, your money is working harder than you are.
How does inflation affect my savings and investments?+
Inflation reduces the real purchasing power of your money over time. Your nominal pot — the headline figure — may grow steadily, but what it can actually buy in the future is less. For investments, what matters is your real return: your annual return minus inflation. For cash savings, inflation can exceed the interest rate entirely, meaning you lose purchasing power even as your balance grows.
Is it better to overpay my mortgage or invest?+
The key question is whether your mortgage rate is higher or lower than your expected investment return. Overpaying gives a guaranteed, risk-free saving at your mortgage rate. Investing targets a higher return — but with uncertainty. Always check for Early Repayment Charges before overpaying. Use our Mortgage vs ISA calculator to model your own numbers.
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Platforms you may want to explore

HL
Hargreaves Lansdown
A UK-regulated investment platform where you can open a Stocks & Shares ISA and start investing. FCA-regulated. Capital at risk.
Find out more →

This is not a recommendation. The platform listed above is provided for information only. Please research your options and consider your personal circumstances before opening any account. The value of investments can go down as well as up. Capital at risk.