Time Value of Money (Future Value/Annuity)

Question

So I found this popular solution online (in the image above, below the question) and I was wondering why they chose this process.

I think I get the process for the solution above but does my attempt work as well?

My Attempt:

When I saw the problem I thought about calculating the Future Value of $$60,000 over 10 years @ 10% interest and comparing it to the Future Value of Annuity of a $10,000 payment over 10 years @ 10% interest.

I can show calculations, but isnt this method more straight forward?

Answer 1

As stated by @quasi

"your method of calculating FVA is identical to theirs. The took FVA, divided it by (1.1)10(1.1)10 and compared it to 6060. One division, one comparison. You took 6060, multiplied it by (1.1)10(1.1)10, and compared it to FVA. One multiplication, one comparison."