I know I know this has been answered 500 times but none of the answers make sense to me

I am asking about question 3 B on EOC reading 49

In the steps after we calculated the present value of both currencies, the answer says we should convert that amount to the equivalent of $1 notional principal; that is, 1/$1.41: 1.016(1/1.41) = £0.7206. Now convert to dollars at the current exchange rate $1.35/£: 0.7206(1.35) = $0.9728.

Why do we need to convert that amount to notional pricipal???

oh is the first conversion calculating how much you invested in the begining for the swap and the second is calculating how much this investment worth at this moment?

I wouldn’t call it investment. In a currency swap you give your principal today and then receive it at expiry at the same rate, i.e. there is no exchange rate gain/loss.

However, the net interest payments are calculated using current exchange rates. So the answer to your question (why we go back and forth) is to account fo the exchange rate movement as well.

Convert this amount to the equivalent of $1 notional principal; that is, 1/$0.86: 1.0068(1/0.86) = €1.1707.

see part of the answer in question 4, can you help me understand excatly how you use 1.0068 euro divided by the exchange rate and come out again as euro??

1.0068 is not money. It is a factor for one unit of notional. So if the notional is 10m, then the PV will be 10,006,800. For Euro notional, this means €11,707,000 or $9,600,000.

The reason this is confusing is because both in EUR and USD cases we used a notional principal of 1 but we know in this currency swap the notionals were €10,000,000 and $ 8,600,000 that changed hands and we expect to reverse this same amounts at the expiration. In that regard the notionals are not simply 1:1 but incorporate initial exchange rate. The EOC assumes a notional of 1 in both cases but immediately corrects it using the historic exchange rate. It then proceeds to calculates the value after 30 days with new exchange rates.