A number that goes up is not the same as getting richer

Every figure on a statement is nominal

A bank balance counts units of currency. So does a salary, a house price, a pension projection and every number in this catalogue’s money tools.

None of them counts what the money buys, and that is the thing anybody actually wants to know. The conversion between the two is inflation, and treating it as a footnote is how a plan that adds up produces a disappointing outcome.

The distinction has a standard vocabulary worth using precisely:

• Nominal — the number on the statement. Units of currency.
• Real — the same quantity expressed in what it buys, usually stated in some reference year’s money.

A savings account paying 2% while prices rise 3% has a positive nominal return and a negative real one. The balance grows every year and buys less every year, and both of those statements are true at once.

The gap compounds, which is the part that surprises people

A single year of 3% inflation is easy to shrug at. Twenty is not, because it is not 60%:

Years at 3%	What 1,000 buys
1	970.87
5	862.61
10	744.09
20	553.68
30	411.99

What 1,000 buys

553.68

What you would need

1,806.11

Years from now

20

Every value

Years from now	What 1,000 buys	What you would need
1	970.87	1,030
2	942.6	1,060.9
3	915.14	1,092.73
4	888.49	1,125.51
5	862.61	1,159.27
6	837.48	1,194.05
7	813.09	1,229.87
8	789.41	1,266.77
9	766.42	1,304.77
10	744.09	1,343.92
11	722.42	1,384.23
12	701.38	1,425.76
13	680.95	1,468.53
14	661.12	1,512.59
15	641.86	1,557.97
16	623.17	1,604.71
17	605.02	1,652.85
18	587.39	1,702.43
19	570.29	1,753.51
20	553.68	1,806.11
21	537.55	1,860.29
22	521.89	1,916.1
23	506.69	1,973.59
24	491.93	2,032.79
25	477.61	2,093.78
26	463.69	2,156.59
27	450.19	2,221.29
28	437.08	2,287.93
29	424.35	2,356.57
30	411.99	2,427.26
31	399.99	2,500.08
32	388.34	2,575.08
33	377.03	2,652.34
34	366.04	2,731.91
35	355.38	2,813.86
36	345.03	2,898.28
37	334.98	2,985.23
38	325.23	3,074.78
39	315.75	3,167.03
40	306.56	3,262.04

Thirty years removes nearly 60% of the purchasing power of an amount held as cash. The same mechanism that makes compound interest impressive over long horizons makes inflation brutal over them, because it is the same mechanism.

The figure worth carrying around is the halving time: at 3%, money halves in value in 23.4 years. At 6%, 11.9. At 12%, 6.1. The rule of 72 approximates all three closely enough for conversation and is tuned for the middle of its range.

The two rates divide, they do not subtract

This is the one piece of arithmetic in the topic that is routinely got wrong, and it is got wrong in the generous direction.

8% return against 6% inflation

approximation:  8 - 6              = 2%
exact:          (1.08 / 1.06) - 1  = 1.8868%

Both are compounding factors, and factors combine by multiplying rather than by adding. The subtraction is close at small numbers and drifts as either rate rises — over thirty years on 1,000, it promises 1,811.36 against a true 1,752.01, so it is about a twentieth too generous.

The same shape appears everywhere on this site: an approximation that is fine where it does not matter and wrong where it does.

What this means for a target

A savings goal set at 20,000 in five years is a nominal target. At 3% inflation it will buy what roughly 17,250 buys today — so the plan is correct arithmetic against a slightly smaller goal than it appears to be.

The right response is not to abandon nominal targets. It is to set them in today’s money, because that is the only figure anybody can reason about, and then convert once to see what it will be worth. Guessing at a future number directly hides the assumption; converting states it.

Three practical consequences:

• A return below inflation is a loss, however positive the statement looks. Cash at 2% against 3% inflation loses about 1% of its value a year.
• Long horizons need a real rate, not a nominal one. A thirty-year plan run at a nominal 7% and never adjusted is describing a quantity of currency, not an outcome.
• Fixed-rate debt moves the other way. The amount owed is fixed in nominal terms, so inflation erodes it to the borrower’s benefit — the same number that hurts a cash saver helps a fixed-rate mortgage holder.

The rate you should use is not the published one

A national index is a basket weighted for an average household, and nobody spends like the average.

If rent, energy or childcare are a large share of your spending, your experienced rate can run well above the headline for years at a time — and if you own your home outright and drive very little, below it. The published figure is a starting point and a comparison, not a measurement of you.

Which is why every tool here takes the rate as an input rather than fetching one. A number you chose and can defend is worth more than a national average applied to a household of one.