compound interest equation for annually compounded
[tex]A=P(1+r)^t[/tex]
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
[tex]1550=1000(1+0.055)^t[/tex]
divide both sides by 1000
[tex]1.55=1.055^t[/tex]
take ln of both sides
[tex]ln(1.55)=ln(1.055^t)[/tex]
use ln rule [tex]ln(a^b)=b(ln(a))[/tex]
[tex]ln(1.55)=t(ln(1.055))[/tex]
divide both sides by ln(1.055)
[tex]\frac{ln(1.55)}{ln(1.055)}=t[/tex]
using a calculator, we get that t=8.18544 yrs
so about 8.2yrs
