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For compounded annually
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
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