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15 / 30 hours free childcare calculation

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Hello, I was surprised to learn how my child's nursery calculates the 15/30 hours free childcare. I'm interested if this is standard or if its better/worse than how other nurseries handle it.

The nursery is open 52 weeks per year, Monday to Friday, from 7:30am until 7pm. Closed on bank holidays.
They have different prices depending on when the children attend. (Full day £68, Half day £48, Full week £306). Price includes food / nappies etc.

My child attends 2 full days per week (though the nursery is open for 11.5 hours per day, the child only attends for about 8 hours per day)
So the actual cost is: 2 days per week * £68 per day * 52 weeks / 12 months = £589.33 per month.

From 1st Sept, my child is eligible for the 30 free hours per week.

I had assumed that it would be calculated as;
Actual cost is: 2 days * £68 * 52 weeks / 12 months = £589.33 per month.
The 30 free hours calculated as: (30 hours * 38 weeks / 12 months) * £68 / 11.5 hours = £561.74 per month
Therefore the cost to me would be £589.33 - £561.74 = £27.59 per month


However, the nursery actually calculates the cost as shown below:
Since the child's age is 3, for the 30 hours, the nursery receives £5.15 per hour from the government.
So the 30 free hours are calculated as: £5.15 per hour * 30 hours per week * 38 weeks a year / 12 months per year = £489.25 per month

Therefore the cost to me is £589.33 - £489.25 = £100.08 per month

(Tax free childcare is then considered on the final sum).

I'm interested in feedback from members; how should it be calculated? How is it calculated at your nursery?

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