> the plan is to invest the money in an index fund that on average earns 5% and all dividends are reinvested. I believe 5% is very reasonable on S&P 500.

Yes, 5% is a conservative estimate for the S&P 500.

> What value should I choose for Interest is compounded? Should it be Yearly?

For the kind of rough hypothetical that is this exercise, Yearly compounding is Good Enough.

> This number seems quite high, is it correct?

This is the magic of compounding, which is why investing a little early is so much more important than investing a lot but later.