There is a link between the elements of the KAFA and CA that logically flow (e.g. if there is high investment in Australia, KAFA positive, which means NPY would be negative - outflow of money from Aus to pay foreign investment). Usually, schools will teach this link (since it’s higher level thinking about relationships, cause and effect), but the reason why the BoP balances is much simpler.
The BoP balances since Australia uses a
double entry accounting framework - a transaction can be recorded from 2 perspectives. Consider this (awful) example. A company in China wants to invest in an Australian mining company and pay for a 30% equity share, paid with 100 bananas. This comes under the definition of ‘direct investment’ (over 10%),into Australia. This transaction is recorded as a credit of 100 bananas on the DI section of the KAFA. But due to the transaction, Australia has 100 extra bananas delivered straight from China. We record this as an
import, which is a debit of 100 bananas on our BOGS in the CA.
See how the BoP balances itself because when we made a positive entry on the KAFA, we also made an identical negative entry on the BOGS in the CA. The reason it balances is that for every transaction between Australia and the rest of the world, there are 2 perspectives to look at it through.
Note that the BoP doesn’t
exactly balance - we have net errors and omissions which make the calculations slightly off. Things like tourist expenditure are hard to sum up and count on the BOGS, and things like military expenditure that are confidential may not make it to the BoP, which means that we’ll end up with a +/- balance which is negligible - just a technicality.
Have a look at this website, it might help. The examples may be a bit more complex, but surely more economically relevant than the bananas one.
https://www.rba.gov.au/education/resources/explainers/the-balance-of-payments.html
if you need any clarification, feel free to ask