Question

Please help ASAP

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=7%=0.07
n=2 (semiannualy means 2 times per year)
t=t

$2=(1+ \frac{0.07}{2})^ \frac{t}{2}$
$2=(1+ 0.035)^ \frac{t}{2}$
$2=(1.035)^ \frac{t}{2}$
take the ln of both sides
$ln2=(\frac{t}{2})ln1.035$
divide both sides by ln1.035
$\frac{ln2}{ln1.035} = \frac{t}{2}$
times 2 both sides
$\frac{2ln2}{ln1.035} =t$
use calculator
40.2976=t
nearest tenth
40.3
about 40.3 years