# Find the amount of time? (Checking work?)

• Mar 22nd 2009, 08:19 AM
puzzledwithpolynomials
Find the amount of time? (Checking work?)
Find the amount of tiem required for an investment to double at a rate of 12.3% if the interest is compounded continuously.

My work:
Assume that P=1
Pe^(rt)
1e^(.123t)=2
.123t=ln2
.123t/.123=ln2/.123
=5.64 years

Yea or nay?
• Mar 22nd 2009, 09:15 AM
e^(i*pi)
Quote:

Originally Posted by puzzledwithpolynomials
Find the amount of tiem required for an investment to double at a rate of 12.3% if the interest is compounded continuously.

My work:
Assume that P=1
Pe^(rt)
1e^(.123t)=2
.123t=ln2
.123t/.123=ln2/.123
=5.64 years

Yea or nay?

Your sum is right but I think you need to use

$
A=A_0(1+x)^n$
where

$A = 2A_0$
$x = 0.123$
$n = n$

$2 = (1+0.123)^n$

$nln(1.123)= ln(2)$
$n = ln(2)/ln(1.123) = 5.98 years$
• Mar 22nd 2009, 09:49 AM
HallsofIvy
No, e^(i*pi), that would be "compounded annually". "Compounded continuously" is exactly what puzzledwithpolynomials says. His answer is correct.
• Mar 22nd 2009, 10:14 AM
jonah
Quote:

Originally Posted by HallsofIvy
No, e^(i*pi), that would be "compounded annually". "Compounded continuously" is exactly what puzzledwithpolynomials says. His answer is correct.

I agree; thus I say yea.