Annuities and perpetuities

Sir, could you solve the following please?

1) What is the PV of $1000 to be received for 5 years starting from now at a discount rate of 10%.
– Is it equal to $1000 + $1000 x DF for 4 years at 10% ?

2) What’s the PV of $100 to be received in perpetuity starting from the beg of year 5 at a discount rate of 10%?
– Is it equal to (100 / 0.1 )x Year 3 DF at 10% ?

3) What’s the PV of $100 to be received in perpetuity starting from the beg of year 5, growing at 2% pa, at a discount rate of 10%?
– Is it equal to (100/ 0.1 – 0.02) x Year 3 DF at 10% ?

4) What’s the PV of $100 to be received at the beg of year 5 for 15 years at a discount rate of 10%?
– Is it equal to 100 x Annuity Factor for 15 years at 10% x Year 3 DF ?

These questions might seem a little silly, but I want to make sure that I have grasped the concepts right.
Thanks for the help and kudos for the great job!! 😀