for compounded annually [tex]A=P(r+1)^t[/tex] A=amount total (future) P=present amount r=rate in decimal t=time in years
given A≥11000 P=4000 r=8.25%=0.0825 t=t solve 11000≥4000(0.0825+1)^t divide both sides by 4000 11/4=(1.0825)^t take the ln of both sides ln(11/4)=ln(1.0825^t) ln(11/4)=t(ln(1.0825)) divide both sides by ln(1.0825) (ln(11/4))/(ln(1.0825))=t evaluate 12.76=t it will take 12.76 years, or, to the nearsest whole year, 13 years
