Calculating the best exchange rate for a given currency based on direct conversion vs multiple currency conversion
I am not sure this is the best place to ask this question. Anyways, here it goes. I live in Mauritius and i am travelling to Tokyo soon. So i would like to exchange some currencies before leaving Mauritius, the issue is i am unable to find a simple (mathematical) function that will help me determine what is the best option for me:
Option 1: I exchange my mauritian rupee to USD and then when in tokyo, i exchange the USD to JPY Currently the exchange rate(including all fees) is as follows: 1 USD -> MUR 34.28 and in tokyo 1 USD -> JPY : 106 JPY
And my second option is
MUR to JPY in my country 100 JPY = MUR 31.20
Is there any mathematical way/formula i could use to determine which is the best for me?
Best Answer
Note: This answer does not deal with any exchange commissions or fees, which is what the OP assumed. In the presence of exchange commissions or fees, the answer will be different.
This answer will start with the Maths, and point out some potential pitfalls that your question might have implied.
The Maths
An easy way to see which exchange option is better is to ask, "how much in JPY I can get with a fixed amount of MUR?". In this case, 100 MUR sounds a good unit to use.
In option 1, assuming 34.28 MUR will get you 1 USD (see below for a caveat), and 1 USD will get you 106 JPY. This means 34.28 MUR will get you 106 JPY, and hence 100 MUR will get you (100 / 34.28) * 106 = 309.22 JPY.
In option 2, assuming 31.2 MUR will get you 100 JPY, this means 100 MUR will get you (100 / 31.2) * 100 = 320.51 JPY.
Thus, option 2 is around 3.65% better. That is, you get 3.65 JPY more for every 100 JPY you exchange.
Lookout for the rate quoted for buying/selling currency
You have put the USD-MUR exchange rate as follow:
1 USD -> MUR 34.28
Which raised an eyebrow of mine. Do you mean you get 34.28 MUR for every USD you sell to the exchange, or you have to pay 34.28 MUR for every USD you buy?
If it is the former case you have to be careful, as you are likely to pay more MUR than the quoted number to buy a currency (as exchanges need to make money for a living as well!). While in this case it doesn't change the outcome (option 2 will still be better), for the method to be generally applicable in the future you have to take that into account.
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How do I find the best conversion rate?
The 13 Most Effective Ways to Increase your Conversion RateHow do you work out the exchange rate between two currencies?
To calculate exchange rate, multiply the money you have by the current exchange rate, which you can find through Google or by calling the Department of the Treasury. For example, if you want to convert $100 to pesos when 1 dollar equals 19.22 pesos, then you would have 1,922 pesos after the exchange.How do you calculate direct and indirect exchange rates?
To get the indirect quote, we just need to find the inverse of the prices and then switch their places. So, for an EU resident, the indirect quotation rate for the euro and USD would be (0.7467 \u2212 0.7468). Thus, the new bid (inverse of the direct ask 1.3392) would be 0.7467.Do you multiply or divide to convert currency?
To convert from the base currency, we multiply by the exchange rate. Just like multiplying to apply a commodity price. Indeed, our base currency can be viewed as the commodity in the quote. Say we need to convert \u20ac8m into dollars, by applying the exchange rate EUR/USD 1.25.Currency Exchange Rates - How To Convert Currency
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