Question

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

Answer 1

I'll use my own formula (similar to yours tho)

$A=P(1+ \frac{r}{n})^{nt}$
A=future amount
p=invested
r=rate in decimal
n=number of times per year compounded
t=time in years


so
when will A=2P
subsitute 2P for A
also quarterly means 4 times a year or n=4
and 12%=0.12=r
so

$2P=P(1+ \frac{0.12}{4})^{(4*t)}$
divide both sides by P
$2=(1+ \frac{0.12}{4})^{(4*t)}$
simplify
$2=(1+ 0.03)^{4t}$
$2=(1.03)^{4t}$
take the ln of both sides
$ln(2)=ln(1.03)^{4t}$
$ln(2)=4tln(1.03)$
$ln(2)=t(4ln(1.03))$
divide both sides by 4ln(1.03)
$\frac{ln(2)}{4ln(1.03)}=t$
use calculator
5.86244=t
about 5.9 years

Answer 2

Answer:

5.9

Step-by-step explanation: