Money Exchange

Changing from Currency A to currency B:

Currency A	Currency B
\(x\) units	\(y\) units
1 unit	\(\frac{y}{x}\) units

\[ z\;units\;of\;Currency\;A = \left(z \times \frac{y}{x}\right)\;units\;of\;Currency\;B \]

Below shows the current exchange rate for Singapore Dollars to other currencies.

SG Dollar Exchange Rate

List of World Currency & Their Symbols


Buying & Selling of Currency

In real life, each currency has its buying and selling rates, which vary daily (depending on the country's economy) and also vary between different banks/money-changers.
When we go to a bank/money-changer, we will see a table (for Malaysian Ringgits) like the one below.

Units Used in Exchange Rate	Foreign Currency	We Buy (Buying Rate)	We Sell (Selling Rate)
1	US Dollar	3.015	3.035
1	British Pound	4.880	4.935
100	Chinese RMB	46.000	46.650
1000	Japanese Yen	36.250	36.700

Base Currency: The currency of the country where you exchange your money.

The "buy" column refers to the buying rate for the bank/money-changer (i.e. selling rate for us) and the "sell" column refers to the selling rate for the bank/money changer (i.e. buying rate for us) for the foreign currency stated (i.e. changing between that currency and the base currency).

Changing foreign currency with base currency:
\[Foreign\;Currency = \frac{Money\;to\;exchange\;in\;base\;currency}{We\;Sell\;\left(Selling\;Rate\right)} \times Units\;Used\;in\;Exchange\;Rate\]

Changing foreign currency for base currency:
\[Base\;Currency = \frac{Money\;to\;exchange\;in\;foreign\;currency}{Units\;used\;in\;Exchange\;Rate} \times We\;Buy\;\left(Buying\;Rate\right)\]

Note: Buying Rate \(<\) Selling Rate
The difference between buying and selling rates is how the bank/money-changer earns money from the money changing process.

Examples:

• To exchange \(RM\;500\) to \(¥\):
  \[RM\;500 = \frac{500}{36.700} \times 1000 = ¥\;13,623.98 \]
• To exchange \(¥\;13,623.98\) to \(RM\):
  \[¥\;13,623.98 = \frac{13,623.98}{1000} \times 36.250 = RM\;493.87 \]

Buying & Selling Rate