C2 geometric question

In question 6b, i formed an equation ar^(n-1) < 500. So i got n is 17 therefore should be in year 2016. But i am not sure why the answer in the mark scheme is year 2015? When i do it in a calculator, in year 2015, the value of the machine is still higher than 500?

ar^n-1<500
15000*0.8^n-1<500

0.8^n-1<500/15000

(n-1)log0.8<log(1/30)

n-1>15.24219437

n>15.24219437+1
n>16.24219437

n=17?

Not sure if that is the answer, just the way i would work it out.

yeah i got n=17 too, so it should be in year 2016? but the answer on mark scheme is year 2015

In question 6b, i formed an equation ar^(n-1) < 500. So i got n is 17 therefore should be in year 2016. But i am not sure why the answer in the mark scheme is year 2015? When i do it in a calculator, in year 2015, the value of the machine is still higher than 500?

Value of machine drops during the year, not suddenly at the end of the year.

At the start of 2016 its value was less than 500. At start of 2015 it was above 500. So, it dropped below 500 during 2015

the question said its value drops at the start of the year. So surely at the start of 2016, it drops below 500?

In red - question doesn't say that. It say each year the value drops by 20% of its value at the start of the year. This does not imply a sudden drop after a year.