Money, Explained From the Inside

Tools / Borrow / Chapters 3 and 11

Rate translator

The same “rate” can be quoted monthly, quarterly or yearly, and it does not cost the same. Convert any quoted rate to its effective annual cost.

1 · The idea

Effective annual rate

Divide the quoted yearly rate by the number of compounding periods, add one, raise it to the number of periods, subtract one.

The formula

EAR = (1 + i/m)^m − 1

i
quoted (nominal) annual rate, as a decimal
m
times per year that interest is added
EAR
what a year of borrowing or saving really adds up to

2 · A worked example

A card quoting 18% a year, charged monthly, is not 18%: (1 + 0.18/12)^12 − 1 = 19.56%. Over a year, $1,000 of debt grows to $1,196.

3 · Now use your own numbers

Change anything. The result updates instantly.

Effective annual rate
19.562%
Quoted rate
18.00%
Interest in one year on $1,000
$195.62
Extra cost from compounding
1.562%Effective minus quoted
Interest addedEffective rateOn your amount
Yearly18.000%$180.00
Half-yearly18.810%$188.10
Quarterly19.252%$192.52
Monthly19.562%$195.62
Daily19.716%$197.16

What this means

The quoted rate is a label; the effective rate is the price. When comparing two offers, compare effective rates, never labels.

The table shows what the same quoted rate becomes at each frequency. The more often interest is added, the more it costs you (or earns you).

Illustrative, not personal advice. Inspired by Chapters 3 and 11 of Money, Explained From the Inside. Your figures stay in this browser. Real products add terms, taxes and conditions that this simple model leaves out.

4 · Take care

What this tool can’t see

  • Fees and charges are not in this rate: use “True cost of a loan” for those.
  • More frequent compounding raises the effective cost of debt and the effective return on savings alike.

5 · Go further

Where this fits

See it in a life:

DavidIncome without wealth

Private to this device. Nothing is sent anywhere.

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