Timing of cash flow DCF

Dear Sir,

I am a bit confused about the timing of cash flow DCF, please correct me if I am wrong.

There is a question on BPP exam kit saying:

what is the NPV of lump sum of $910,000 take in a year time at the cost of capital of 10%?

I use the discount factor of the year 1 ( which is was 0.909 whereas the book answer discount at the rate of year 2 0.826)

Could you please explain why?

Is it not the same rule that we apply to the annuity question like: 90,000 receive a 5 year annuity starting in 3 year’s time where we start counting from year 3.

You might have it explained in the lecture. I watch the lecture and I though it was clear to me, but this question it confused me.

Really appreciate your help

Thanks

Gabriella