Grow your savings — see the future value with compounding.
Simple interest pays only on the original amount. Compound interest pays on the accumulated balance, so each period's growth becomes part of the base for the next. The effect is barely visible early on and dramatic late on.
Future value = P × (1 + r ÷ n)n × t
where P is the starting amount, r the annual rate, n the compounding periods per year, and t the number of years.
The consequence is that time matters more than rate. An investment growing at 7% doubles in roughly ten years, quadruples in twenty, and grows eightfold in thirty. Most of that final total arrives in the last third of the period, which is exactly why starting earlier beats contributing more later.
Divide 72 by the annual percentage rate to estimate how many years it takes for money to double. At 6% that is twelve years; at 9%, eight years; at 12%, six years. The approximation is accurate enough for mental arithmetic across the range of returns most people encounter.
It works in reverse too. At 3% inflation, prices double — and the purchasing power of cash halves — in about 24 years.
Any compound projection assumes a constant rate, and real returns are never constant. That matters more than it seems, because volatility drags on compounded outcomes. A year of +50% followed by a year of −50% leaves you down 25%, even though the arithmetic average of those two years is zero.
The projection is also before tax and fees. An annual management charge of 1% might sound trivial, but over thirty years it can consume a meaningful share of the final balance, because every pound taken in fees is also a pound that stops compounding. Inflation erodes the rest: a nominal 7% return with 2.5% inflation is a real return closer to 4.4%.
Treat the result as an illustration of how compounding behaves rather than a forecast. Using a conservative rate produces a plan that survives disappointment; using an optimistic one produces a plan that only works if you get lucky.