P2 logarith qquestion doubt please help

[cashem'up]

Jack is saving for a new car which will cost $29000 . He saves by putting $400 a mmonth into a savings account which gives 0.1% interest per month . After how many months will hee be able to buy his car.
 pg 40 chapter 3 question8 exc 3C P2

[astarmathsandphysics]

When I come back

[astarmathsandphysics]

Jack is saving for a new car which will cost $29000 . He saves by putting $400 a mmonth into a savings account which gives 0.1% interest per month . After how many months will hee be able to buy his car.
a GEOMetric series
S_n=a(1-r^n)/(1-r)
29000=400(1-1.001^n)/(1-1.001)
1-1.001^n=29000/400*(-0.001)=-.0725
1.001^n=1+0.0725
n=ln(1,0725?/ln(1.001)=70.027
so n=71