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?

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- Mar 22nd 2009, 07:19 AMpuzzledwithpolynomialsFind 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, 08:15 AMe^(i*pi)
Your sum is right but I think you need to use

$\displaystyle

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

$\displaystyle A = 2A_0$

$\displaystyle x = 0.123$

$\displaystyle n = n$

$\displaystyle 2 = (1+0.123)^n$

$\displaystyle nln(1.123)= ln(2)$

$\displaystyle n = ln(2)/ln(1.123) = 5.98 years$ - Mar 22nd 2009, 08:49 AMHallsofIvy
No, e^(i*pi), that would be "compounded annually". "Compounded continuously" is exactly what puzzledwithpolynomials says. His answer is correct.

- Mar 22nd 2009, 09:14 AMjonah