Currency Exchange Rates

The exchange rate of the Athelstan riyal (ATH) with the British pound is 9.00 ATH/GBP. The exchange rate of the Mordred ducat (MOR) with the U.S. dollar is 2.00 MOR/USD. If the USD/GBP exchange rate is 1.50, the ATH/MOR cross rate is closest to:

explanation: The ATH/MOR cross rate = 9.00 ATH/GBP × (1 / 1.50) GBP/USD × (1 / 2.00) USD/MOR = 3.00 ATH/MOR.

Why 1/1.50 GBP/USD? this pair is not asking , so why not 1.50usd/gbp?

You are selling the top currency, to purchase the bottom currency. The end effect you want to sell ATH to purchase MOR. You start that by selling 9 ATH for 1 GBP. You are told the USD/GBP rate is 1.5, but you already have GBP, you do not need to purchase more, you need to take that and purchase USD. so you 1/(USD/GBP) and that gives you the GBP/USD rate you need. You take that USD and you need to convert it to MOR, but the rate is given as MOR/USD, so again you have to 1/(MOR/USD) to get the correct rate.

That gives you: .9*.6667*.5=3

You have to calculate cross-currency rate ATH/MOR over 2 currencies, USD (MOR) and GBP (ATH). Since you have GBP as base currency at pair USD/GBP and again you have USD as base currency at pair MOR/USD you have to calculate reciprocal value to reach direct quotation.

Anyway, the simpliest approach is using division instead reciprocal value at pairs with same currency in nominator or denominator (price/base) at each currency pair. Thus:

ATH/GBP : USD/GBP : USD/MOR = 9:1.5:2=3

All curency pairs are important in equation because USD quoted to MOR and GBP qouted to ATH. ATH and MOR are not quoted as currency pair so you have to calculate rate using cross-rate through USD and GBP.

I’m not sure how everyone is approaching these but I would find them very confusing if I did not remember “conversion of units” from science class.

remember… If you have a value that is 5ft and want it to convert it into inches … it looks like this

5 feet x 12 inches/ foot = 60 inches

I was trying to show that the logic comes from setting it up so when you multiply the ratios, the units you don’t want gets canceled, leaving you with the correct conversion in the correct units.

Converting currency is just like this… Sometimes when you want to convert, you have to use the inverse to get the desired canceling. as in step one above, you must use GBP/ USD rather than USD/ GBP in order to get GBP to cancel.

If this was just confusing, please ignore it!

When you use ATH/GBP : USD/GBP : USD/MOR (so 3 step crossing just cancel each repeating to get final outcome) so:

ATH/GBP : USD/GBP : USD/MOR = ATH/MOR. What is confusing here? Consider ATH is currency and MOR is banana or whatever…

^ good! I’m glad I was able to communicate what I was thinking.

Just watch out on order Price/Base and vice versa. F.ex. if you have pairs USD/GBP USD/EUR and EUR/HRK to reach GBP/HRK you get to divide first pair and then multiply second:


I wrote an article on this that may be of some help: