Question

If $7000 is placed in account with an annual interest of 5.5% how long will it take the amount to double if the interest is compounded annually?

Answer 1

$A=P(1+ \frac{r}{n})^ \frac{t}{n}$
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