Preambles
Explain this calculation. Why isn’t this more than a 100% fall?
the naira fell from about 460 to roughly 1,500 per dollar, a loss of more than 60%.
This is one of the most common sources of confusion in exchange-rate discussions.
The key point is that a currency cannot lose more than 100% of its value, because a 100% loss would mean it is worth zero.
Let’s work through it.
What happened?
The exchange rate moved from:
- ₦460 per US$1
to - ₦1,500 per US$1
At first glance, it looks like the Naira got worse by:
\frac{1500 - 460}{460} \times 100
= \frac{1040}{460} \times 100
= 226%
So people often say:
“The dollar rose 226% against the Naira.”
That calculation is correct.
But that is not the same thing as saying the Naira lost 226% of its value.
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Why not?
Exchange rates can be expressed in two opposite ways.
Method 1: Naira per Dollar
Before:
- US$1 = ₦460
After:
- US$1 = ₦1,500
The cost of a dollar increased by 226%.
This tells us how much more Naira is needed to buy a dollar.
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Method 2: Dollars per Naira
Now let’s ask:
How many dollars does one Naira buy?
Before:
1/460 = 0.002174
A Naira bought about:
US$0.00217
After:
1/1500 = 0.000667
A Naira bought about:
US$0.000667
Now calculate the fall:
\frac{0.002174 - 0.000667}{0.002174}
\times 100
= 69.3%
So:
The Naira lost about 69% of its value against the dollar.
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Simple analogy
Suppose a loaf of bread costs:
- ₦460 yesterday
- ₦1,500 today
The bread price increased by 226%.
But the purchasing power of ₦1 did not fall by 226%.
Instead:
- ₦460 used to buy one loaf.
- Now ₦460 buys only:
460/1500 = 30.7%
of a loaf.
So the purchasing power fell by about:
100 - 30.7 = 69.3%
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The general rule
If an exchange rate moves from A to B:
Currency depreciation
1 - \frac{A}{B}
Currency appreciation of the other side
\frac{B-A}{A}
Using ₦460 → ₦1,500:
Dollar appreciation
\frac{1500-460}{460}
=226%
Naira depreciation
1-\frac{460}{1500}
=69.3%
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Therefore
Both of these statements are true:
- The dollar became about 226% more expensive in Naira terms.
- The Naira lost about 69% of its value against the dollar.
The reason it is not “more than 100% fall” is that a currency’s value cannot fall below zero. The maximum possible loss is 100%, while the exchange rate itself can rise without limit. A move from ₦460/ to ₦1,500/ means the dollar became 3.26 times as expensive, not that the Naira became less than worthless.