Question

If the GBP quote is USD 1.2772-87 answer the following questions and please provide formulae and show all workings.

a. If you converted $20,000 to GBP and then back to USD, what would be its value in USD?

b. If you are able to buy pounds at the bid rate and sell them at the ask rate, how many USD would you need to earn $1,750 on a round-trip transaction (buying GBP for USD and then selling the GBP for USD)?

Answer 1

a) GBP quote is USD 1.2772-87. It means that if you sell 1 pound, you will get $ 1.2772. And if you want to purchase 1 pound, you will have to give $ 1.2787.

So, if you convert $20000 to GBP, it means you want purchase GBP, you will get

= 20000/1.2787 = GBP 15640.88

Now, you convert the same in USD, it means that you want to sell GBP, you will get

= 15640.88 * 1.2772 = $ 19976.54

So, $20000 Xcovnerted to GBP and back to USD, the value of USD will be $ 19,976.54

b) Bid = 1.2772 USD / GBP

Ask = 1.2787 USD / GBP

Let USD be X.

So, first we will convert USD to GBP @ bid rate = X/1.2772

Now, we will convert back GBP to USD @ ask rate = X/1.2772*1.2787

So, to get profit of $1750,

Profit = (X/1.2772*1.2787) - X

1750 = 0.0015X/1.2772

X = 1750 * 1.2772/0.0015

= $ 1,490,066.67