What is the Rule of 72?

The Rule of 72 is a shortcut to estimate how long it takes to double an investment. Divide 72 by the annual interest rate: 72 ÷ 8% = 9 years to double. It works for any compounding growth rate — including inflation (72 ÷ 3% inflation = 24 years for purchasing power to halve). The rule is most accurate for rates between 4% and 12%.

How does compound interest differ from simple interest?

Simple interest is calculated only on the principal. Compound interest is calculated on principal plus previously earned interest — interest earns interest. Over long periods, the difference is dramatic. £10,000 at 8% simple interest for 30 years: £34,000. At 8% compound: £100,627. Compounding is why starting to invest early matters so much more than investing large amounts late.

How does compounding frequency affect investment growth?

More frequent compounding produces slightly higher returns. £10,000 at 10% for 10 years: annual compounding = £25,937; monthly = £27,070; daily = £27,179. The difference between monthly and daily is small, but monthly vs. annual is meaningful at large balances. Most investment accounts compound daily; savings accounts typically compound monthly or daily.

What interest rate do I need to double my money in 10 years?

Using the Rule of 72: divide 72 by your target years. To double in 10 years: 72 ÷ 10 = 7.2% annual return required. To double in 7 years: 72 ÷ 7 = 10.3%. To double in 5 years: 72 ÷ 5 = 14.4%. These are total return figures — a diversified equity portfolio has historically returned 7–10% annually over long periods (before inflation).

How Compound Interest Really Works: The Rule of 72 and the Numbers That Matter

Why Einstein Allegedly Called Compound Interest the Eighth Wonder of the World#

Whether Einstein actually said it is disputed by historians, but the sentiment captures something real: compound interest is the mechanism by which money grows exponentially rather than linearly. Simple interest calculates returns only on the original principal: £1,000 at 5% simple interest earns £50 every year regardless of how long you leave it. Compound interest calculates returns on both the principal and all previously earned interest: the same £1,000 at 5% compounded annually earns £50 in year one, £52.50 in year two (because interest is now calculated on £1,050), and so on. The difference is small in the early years — and enormous over decades. Use the Compound Interest Calculator at allio.tools/compound-interest-calculator/ to see the gap at any time horizon.

The Formula Behind Compound Interest#

The compound interest formula is: A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal (initial amount), r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. For £1,000 invested for 20 years at 7% compounded annually: A = 1000 × (1 + 0.07/1)^(1×20) = 1000 × 1.07^20 = £3,869.68. The same investment compounded monthly: A = 1000 × (1 + 0.07/12)^(12×20) = £4,038.74. More frequent compounding adds 4.4% extra return over 20 years in this example — not enormous, but the difference grows with time and rate.

The Rule of 72: Mental Maths for Doubling Time#

The Rule of 72 is a simple approximation: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6% annual return: 72/6 = 12 years to double. At 8%: 72/8 = 9 years. At 3% (approximate savings account rate): 72/3 = 24 years. The rule works because it approximates the natural logarithm calculation required for precise doubling time. It is accurate to within one or two years for rates between 3% and 20%. The rule works in reverse too: if you need to double your money in 8 years, you need a rate of approximately 72/8 = 9% per year. This simple shortcut changes how you evaluate financial products at a glance.

Compounding Frequency: Annual, Monthly, Daily — Does It Actually Matter?#

Compounding frequency has a real but diminishing effect as frequency increases. The difference between annual and monthly compounding at 7% over 20 years is approximately 4.4% — meaningful but not transformative. The difference between monthly and daily compounding at the same rate is under 0.2%. For practical investing purposes, monthly compounding (standard for most savings accounts and bonds) versus daily compounding (used by some savings accounts) is almost irrelevant. Annual compounding (used in many simple investment illustrations) slightly understates long-term returns. The number that matters most is the rate itself — a 1% improvement in annual return over 20 years at £10,000 produces £2,190 more than the difference from switching compounding frequency.

The Devastating Mirror Effect: Compound Interest on Debt#

Compound interest on savings grows your wealth exponentially. Compound interest on debt grows what you owe exponentially — and typically at rates far higher than any investment. Credit card rates of 20–25% APR compound monthly. At 22% APR: a £2,000 credit card balance left unpaid for 5 years grows to £5,843 — nearly three times the original debt. At 7% investment return: the same £2,000 grows to £2,806 over 5 years — less than half the credit card growth. This is why eliminating high-interest debt provides a guaranteed return equivalent to the debt's interest rate: paying off 22% debt is equivalent to earning 22% on an investment. The Loan Calculator at allio.tools/loan-calculator/ shows the total cost of any credit over its full term.

Regular Contributions: Where Compound Interest Becomes Transformational#

The compound interest formula above assumes a single lump-sum investment. Regular contributions change the picture dramatically. £200 per month invested at 7% annually for 30 years produces £242,000 — despite only £72,000 of actual contributions. The remaining £170,000 is compound growth. Starting 10 years earlier with the same monthly amount produces £494,000 — more than double — demonstrating that time in the market is more valuable than the amount invested. The practical implication: starting a regular investment programme at 25 versus 35 is worth more than doubling the monthly contribution at 35. Earlier is almost always better than larger. The Compound Interest Calculator at allio.tools/compound-interest-calculator/ models lump-sum investments; for regular contribution modelling, use the Investment Return Calculator.

Inflation: The Silent Counter to Compound Growth#

Compound interest grows your nominal balance — the number on your statement. Inflation erodes your real purchasing power. If your investment earns 7% annually and inflation runs at 3%, your real return is approximately 4% (the precise calculation uses the Fisher equation: real rate ≈ (1 + nominal)/(1 + inflation) - 1 ≈ 3.88%). Over long time horizons, this matters enormously: £100,000 in nominal terms in 30 years buys significantly less than £100,000 today if inflation averaged 3%. The Inflation Calculator at allio.tools/inflation-calculator/ shows the real value of any future sum in today's money. Plan for real returns, not nominal ones — the difference between 7% nominal and 4% real over 30 years on £10,000 is the difference between £76,123 and £32,434 in today's purchasing power.