Why compound growth is magic — and why the line goes up, not straight

The shape of the line

Put £1,000 in a savings account at 5% per year. After year 1 you have £1,050. After year 2 you have £1,102.50. After year 3, £1,157.63. After year 10, £1,628.89. After year 20, £2,653.30. After year 30, £4,321.94. The simple-interest version — the one your brain imagines when you hear "5% a year" — gives you £1,500 after 10 years, £2,000 after 20, £2,500 after 30. The compound version is bigger than that in every year after the first, and the gap grows the further out you go. That is the magic. You did exactly the same thing each year. You didn't add any new money. The only difference is that the interest from this year becomes part of the base that next year's interest is calculated on.

The rule of 72

For small interest rates, money doubles in roughly 72 ÷ rate years. At 5%, that is 14.4 years. At 7%, about 10.3 years. At 10%, 7.2 years. The rule is approximate but useful — it lets you size up a "5% APY" or "7% annual return" in 10 seconds without doing the math. For a mortgage, the rule works in reverse: at 6% interest, the balance doubles in 12 years. (That is the bad kind of doubling.)

Why people underestimate it

Two reasons. The first is that the early years are unimpressive. The difference between simple and compound interest over 5 years on £1,000 at 5% is £28. That is not exciting. It doesn't feel like magic. The second is that the late years are unimaginable. The doubling at year 14 produces £2,000. By year 28 it is £4,000. By year 42, £8,000. Most people are not planning in 14-year chunks.

Why this matters more for early savers than late

Someone who starts saving £100/month at age 25 and stops at age 35 (contributing for 10 years) ends up with more at age 65 than someone who starts at age 35 and contributes for 30 years. This is the most counter-intuitive and most important result in personal finance. The first decade of contributions earns interest for 40 years. The last decade of contributions earns interest for 0 years. Time, not contribution, is the active ingredient.

When compounding works against you

It works identically on debt. A credit card balance at 24% APR doubles in roughly 3 years if you pay only the minimum. Minimum payments are set to maximise how long the balance survives, because the issuer earns interest on the outstanding balance for as long as possible. Compounding is not good or bad. It is a process. The question is which side of the process your money is on.

What a "compound interest calculator" should tell you

The balance at each year, not just the final number. The interest earned versus the contributions made. (You want this gap to be wide.) The doubling time at the given rate. The effect of adding a fixed monthly contribution. (This is where the real growth comes from, not the rate.) The future value in today's money, not just nominal terms.