Find the amount of time? (Checking work?)

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March 22nd 2009, 07:19 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?
March 22nd 2009, 08:15 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

$<br /> A=A_0(1+x)^n$ where

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

$2 = (1+0.123)^n$

$nln(1.123)= ln(2)$
$n = ln(2)/ln(1.123) = 5.98 years$
March 22nd 2009, 08:49 AM
HallsofIvy

No, e^(i*pi), that would be "compounded annually". "Compounded continuously" is exactly what puzzledwithpolynomials says. His answer is correct.
March 22nd 2009, 09:14 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.

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