Question 319968
Find the doubling time for money invested at 3% compounded continuously. 
:
The continuous interest formula
{{{P*e^(rt)}}} = A
where
P = initial amt (in this problem we will use 1)
r = interest rate in decimal form, (.03)
t = no. of years
A = resulting amt; (in this problem it will be 2)
:
{{{1*e^(.03t)}}} = 2
using natural logs
{{{ln(e^(.03t))}}} = ln(2)
log equiv of exponents
.03t*ln(e) = ln(2)
Find the nat log of both side. (nat log of e = 1)
.03t = .693
t = {{{.693/.03}}}
t = 23.1 yrs to double at 3%
:
:
Confirm this on a calc: enter e^(.03*23.1) results: 1.9997 ~ 2