compound interest equation for annually compounded

A=final amount
P=principal
r=rate in decimal
t=time in years
given that
A=1550
P=1000
r=5.5%=0.055
find t

divide both sides by 1000

take ln of both sides

use ln rule


divide both sides by ln(1.055)

using a calculator, we get that t=8.18544 yrs
so about 8.2yrs