Converting currencies

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Below, we explain the theory of how exchange rates work.

Variability of exchange rates

The purchase/sale of currencies occurs in a free market. The price (exchange rate) is based on the law of supply and demand. The differences in the exchange value can be more or less important according to the fluctuations of the exchange rate.

The exchange rates in the following examples, are not the actual daily ones, but are fictitious to explain the problematic.

The exchange rate
The exchange rate refers to the basic currency. There are always two different exchange values between two currencies, according to the currency that is used as the basic currency.

For the USD and Euro currency, there are therefore two different exchange rates:

• If the basic currency of the exchange is EUR then the exchange rate is 1.32030
  1 Euro (EUR) corresponds to 1.32030 US Dollars (USD)
• If the basic currency of the exchange is USD then the exchange rate is 0.75800
  1 US Dollar corresponds to 0.75800 Euros

In the current document, the Euro will be regularly used as the basic currency, to which other currencies will be compared.

Inverse exchange rate
Having the exchange of EUR/USD at 1.32030, it is possible to find the exchange rate of USD/EUR by dividing 1 by the exchange rate.

The exchange values calculated with an inverse exchange can turn out to be different from the original one due to rounding.

Don't use inverse exchanges rates in order to avoid differences.
For the transition to the Euro, for example, the use of inverse exchange rates was prohibited.

Multiplier
There are currencies that have very large exchange rate values.

Always on January 1^st

• 1 US Dollar = 670,800 Turkish Lira
• 1 Turkish Lira (TRL) = 0.00000149 US Dollar (USD)

Instead of using that many zeros, it can be said that

• 1000 Turkish Lira (TRL) = 0.00149 US Dollar (USD)

In this case, the multiplier is 1000 instead of 1.

Preciseness 
As a rule, an exchange rate is specified with a preciseness of at least 6 figures after the decimal.
There are, however, cases where it is necessary be more precise.

• 1 Turkish Lira (TRL) = 0.00000149 US Dollar (USD)

When the preciseness is changed and the exchange is rounded in a different way, the amounts also change. The preciseness with which the exchange is specified is very important.

Minimum denomination
  Especially for paper money, minimum denominations are used. As a rule the lowest denomination for Swiss francs is five centimes (0.05). When an exchange occurs, for example EUR/CHF:

1 EUR = 1.60970 CHF

Calculation of exchange rates and values
When the Euro is the basic currency

The exchange factor for EUR/USD is 1.32030
1 Euro (EUR) is equal to 1.32030 US Dollars (USD).

Calculation of the exchange value:
Multiply the basic currency amount by the exchange factor:

EUR 100 x 1.32030 = USD 132.03

Calculate the basic currency amount:

Divide the destination currency by the exchange rate:

USD 132.03 / 1.32030 = EUR 100

Calculate the exchange factor:

Divide the basic currency amount by the destination currency amount:

EUR 100 / USD 132.03 = 0.7574   

Exchange rates for purchases and sales
Banks carry out the purchase and sale of currencies and include a transaction margin. They apply different exchange rates depending on whether a determined currency is being bought or sold.

Sale: the bank receives domestic money and provides (sells) foreign money.

Purchase: the bank receives (purchases) foreign money and provides domestic money.   

Currency exchange and banknotes exchange (premium)
Currency exchange: exchange for scriptural transactions (from one account to the other).
Banknote exchange: exchange for banknotes.
Premium: commission for converting a scriptural amount to cash.

To exchange currency, the banks maintain a lesser margin (the difference between purchase/sale) compared to exchanging banknotes. When a scriptural value is to be transformed (credit on the account) into cash currency, the bank applies a commission, called a premium.   

Differences when changing back to basic currency 
When an amount is exchanged into another currency, it is expected that the reverse exchange will result as identical to the original amount .

However, you do not always come up with the same amount when converting currency back. Because of rounding errors, there may be cases where the same return value cannot be obtained.

Differences of totals through splitting 
The total exchange value of the components of an amount does not always result in the same exchange value as the overall amount.
In this example, the amount of 2.16 EUR produces an exchange value in USD of 2.85. By splitting the amount and adding the two exchange values, 2.84 will result.

These mathematic differences cannot be eliminated if they are not recorded properly.