\(A=P(1+ \frac{r}{n})^ \frac{t}{n}\)
A=future amount
P=present amount
r=rate in decimal
n=number of times per year compounded
t=time in years
how many years to double
basically
A=2P at t=?
so we can simplify and ignore the pricipal given and do
\(2=(1+ \frac{r}{n})^ \frac{t}{n}\)
r=5.5%=0.055
n=1
t=t
\(2=(1+ \frac{0.055}{1})^ \frac{t}{1}\)
\(2=(1+ 0.055)^t\)
\(2=(1.055)^t\)
take the ln of both sides
\(ln2=t(ln(1.055))\)
divide both sides by ln1.055
\(\frac{ln2}{ln1.055}=t\)
use calculator to aproximate
12.9462=t
about 12.9 years
