Behind the scenes, how to profit off buying USD when account is in USD?

I've been working on understanding pip-worth calculations. I can calculate the (pip/rate) * (notional amount) formula but I would like to understand how to derive it.

Brokers must have various currencies in banks to allow me to buy USDJPY when all I have in my account is USD, correct?

If I buy one 10k lot of USDJPY at 130.26, the broker holds $50 of my money as a margin and then transfers $10k worth of yen (JPY 1,302,600 in this example) into USD.

If I later sell USDJPY at 130.36, the broker changes the $10k back into JPY which at this point becomes JPY 1,303,600. The broker must now use the original exchange rate of 130.26 to calculate how much I have gained, correct?

I guess this only makes sense because if they used the new exchange rate my account balance would not change at all. I'd just like someone to verify this or point out where my thinking went wrong if I'm incorrect.

Thanks,

Forexwindo

Usually trades are aggregated, so your trade is paired against someone else that is selling USD and buying JPY. Only the net trades are passed out to the market and used to cover the net position risk. Brokers have "liquidity providers" that allow them to take these trades.

But yes, if you buy USDJPY you are borrowing and selling JPY at the current JPY exchange rate and buying USD at the current exchange rate for the trade. You now hold a short position on the JPY and a long position on the dollar.

When you close the position you make the opposite trade, buying JPY with the dollars you bought earlier and returning the JPY back to where you borrowed it. If the value of the JPY has gone up relative to the dollar then you lose money (pay more for the JPY), if the value of the JPY has gone down relative to the dollar you bought then it doesn't cost as much to buy it back and you come out ahead.