# 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?

• Ask yourself: if I exchange 1000 MUR, how many JPY do I get in each case? It will be obvious that the second option is much better. – jcaron Jan 16 at 8:59
• Also, you may want to check the various fees for using a VISA or MasterCard debit card to withdraw money from an ATM in Japan. It is often the best option, though it can vary quite a lot. Fees usually include foreign withdrawal fees, and the "spread" over the interbank exchange rate. – jcaron Jan 16 at 13:05
• Please note that 1 USD- > MUR 34.28 does NOT mean that 34.28 MUR -> 1 USD. There are significant differences because of fees and commission. In fact optimizing for fees will probably a better return than optimizing for exchange rates. – Hilmar Jan 16 at 13:31

Simply compute how much JPY you get for the same amount in MUR, and you will be all set.

In the first case, 1000 MUR will give you (1000/34.28) = 29.17 USD, which will then give you (29.17 * 106) = 3092 JPY, so the overall exchange rate is 1 MUR = 3.092 JPY.

In the second case, 1000 MUR will give you (1000*100/31.20) = 3205 JPY (exchange rate 1 MUR = 3.205 JPY).

The second option is clearly better, you get more JPY for the same amount.

• this is what i was looking for. Accepted as best answer – Margue Jan 16 at 9:04
• Gah I lost by 3 minutes :P – B.Liu Jan 16 at 9:06
• @Gah still i find your answer useful. – Margue Jan 16 at 9:10

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.

# 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.

• thanks for the detailed explanation. and yes- its 34.28 MUR for every USD i buy. – Margue Jan 16 at 9:09