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

1. ## 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?

2. 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

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

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

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

$\displaystyle nln(1.123)= ln(2)$
$\displaystyle n = ln(2)/ln(1.123) = 5.98 years$

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

4. 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.