how long does it take for a deposit of $P to double to 10% interest compounded continuously?

Question

directrix · Answer

A = P e ^(rt) is the formula for continuous compounding of interest 
Let P = amount invested and 2P the desired amount after t years at 10% interest
(2P) = P e ^ (.1t)
2 = 1 * e ^ (.1t)
2 =  e ^ (.1t)
ln(2) = ln (e ^ (.1t))
ln (2) = .1t * ln(e)
ln (2) = .1t * 1
ln (2) = .1t 
t = [ ln(2) ] / (.1)
t = 6.9314 years for principal investment to double

paxpolaris · Answer

$$\Large A=P \cdot e^{rt}$$
r=10/100 =0.1
solve for 't' when A=2P

anonymous · Answer

simple just divide 72 by number of years

anonymous · Answer

it is called as rule of 72

anonymous · Answer

alot of time