£40k a year?! That's more than Eton lol.
It's between £15k and £20k per year for pretty much all good private schools. Add in other costs to do with the school throughout the year, and let's just say it costs £18k a year.
A £60k salary is a £41k a year salary after tax, NI and a 6% pension. If your partner also brought in £60k a year, you'd have a total, real household income of £82k a year. Factor in mortgage/utilities/other costs eating up maybe 65% of your income per month (after tax), and you'd thus have only £28.7k (call it £28k) left on actual luxuries for the whole year.
£18k of £28k on money for 'luxuries', taken up solely to take one child to a private school, is a lot. To answer your question, two people/partners on £60k can indeed just about take their children to a private school. But you'll barely save ANYTHING throughout the year. You'll have enough for holidays from that £10k left to spend on luxuries. But you CANNOT save. And that's more important than anything else. Want an £80k car? You won't have it on two £60k incomes if you take one child to a private school (unless you save for 8-20 years, which is just a depressing thought lol).
What I would personally do is treat myself whilst I'm young, then think of having kids. I want that £80k car, for example. I'd like to be saving £2k a month just for it every month... I've got to get a 6 figure salary, personally. Hopefully before I'm 35 or so ABSOLUTE max (will be much, much sooner if I get into the City). I've genuinely got to wifey a nice, old money girl who herself is well educated and on a good income lol.
Sacrifice by getting a cheaper property/less luxuries, but yes: TWO £60k incomes even in London is theoretically JUST enough to send ONE child to a private school.
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