Why compounding feels slow, then sudden
Compound interest is growth on growth. In the early years it is barely distinguishable from simple interest, which is why saving can feel pointless at the start. The acceleration comes later, and it comes from the accumulated balance rather than from anything you do differently.
The formula
For a lump sum with no further contributions:
A = P × (1 + r/n)^(n×t)where P is what you start with, r the annual rate as a decimal,n how many times a year interest is applied, and t the number of years. Adding regular contributions adds a second term — the future value of an annuity:
A = P × (1 + r/n)^(n×t) + PMT × [((1 + r/n)^(n×t) − 1) ÷ (r/n)]The rule of 72
To estimate how long money takes to double, divide 72 by the annual return. At 6% that is 12 years; at 9%, eight years. It is an approximation, but it is accurate enough for mental arithmetic and it makes the cost of a lower return immediately visible.
Does compounding frequency matter?
Less than people expect. Moving from annual to monthly compounding at 7% adds roughly 0.23 percentage points to the effective annual rate; going from monthly to daily adds almost nothing. The rate, the amount and the number of years dominate. Frequency is a rounding detail by comparison.
Why the inflation figure matters most
A balance decades away is quoted in future money, which buys less than today's money. At 2.5% inflation, purchasing power halves in about 28 years — so a projection that looks impressive in nominal terms can be sobering once adjusted. That is the number in the "in today's money" column, and it is the one worth planning against.
This also explains why cash held in a low-interest account loses value in real terms even though the nominal balance never falls. If the account pays 1% and inflation runs at 3%, you are losing 2% of purchasing power a year while watching the number go up.
Built and maintained by Mohammed Jamil. Found an error in the maths? Email [email protected].