annuity

Good evening…. the following question is very embarrassing …. i cant seem to get the annuity right!!!!

project has the following cash flows:
investments in the first 3 years as below. the labels “year 1”, “year 2”, “year 3” are exactly as given in the question.

year 1 – (immediately) (2500)
year 2 – (1200)
year 3 – (1400)

for the project’s inflow it says:

“annual operating cash flows commence at the end of year 4 and last for a period of 15 years. the annual cash inflows are 970. the required rate of return is 11%”

so i set it up as follows:

year——–0———–1————2———3-
———-(2500)—(1200)—–(1400)——-970 onwards
DF 11%—1———.901——-.812——–.731

Now…AF 3-18 = AF3-15 – AF3
this factor will give me the PV at year 2 (which is actually yr 3) and then i will discount it at the DF for the year 2… my numbers are all wrong

the answer simply does the following:

PV of annuity=970 x 7.191 x .731

7.191 is the AF for period 15 @11%

how/why is he using this?

also, the Df factor shd be 0.812 since PV is at year 2

pls explain.

thank u