# Annual Rate

• Oct 26th 2008, 06:18 AM
dc52789
Annual Rate
What annual rate of interest compounded annually should you seek if you want to double your investment in 5 years?
• Oct 26th 2008, 11:39 AM
Jhevon
Quote:

Originally Posted by dc52789
What annual rate of interest compounded annually should you seek if you want to double your investment in 5 years?

use the compound interest formula:

$\displaystyle A = P \left( 1 + \frac rn \right)^{nt}$

where $\displaystyle A$ is the amount after time $\displaystyle t$, $\displaystyle P$ is the principal, $\displaystyle r$ is the rate of interest, and $\displaystyle n$ is the number of times in is compounded per year

here, $\displaystyle n = 1$ and you need to find $\displaystyle r$. but this is what you want to happen. after 5 years, you want $\displaystyle P$ to become $\displaystyle 2P$. thus you want

$\displaystyle 2P = P \left( 1 + r \right)^5$

now solve for $\displaystyle r$
• Oct 26th 2008, 11:44 AM
dc52789
Quote:

Originally Posted by Jhevon
use the compound interest formula:

$\displaystyle A = P \left( 1 + \frac rn \right)^{nt}$

where $\displaystyle A$ is the amount after time $\displaystyle t$, $\displaystyle P$ is the principal, $\displaystyle r$ is the rate of interest, and $\displaystyle n$ is the number of times in is compounded per year

here, $\displaystyle n = 1$ and you need to find $\displaystyle r$. but this is what you want to happen. after 5 years, you want $\displaystyle P$ to become $\displaystyle 2P$. thus you want

$\displaystyle 2P = P \left( 1 + r \right)^5$

now solve for $\displaystyle r$

I did 2 = (1+r)^5
Is that right so far?
• Oct 26th 2008, 11:46 AM
Jhevon
Quote:

Originally Posted by dc52789
I did 2 = (1+r)^5
Is that right so far?

yes

P is not zero, so we can divide by it
• Oct 26th 2008, 11:54 AM
dc52789
Quote:

Originally Posted by Jhevon
yes

P is not zero, so we can divide by it

So...do I put the square 5 on the two to eliminate the 5 on the other side?
• Oct 26th 2008, 12:00 PM
Jhevon
Quote:

Originally Posted by dc52789
So...do I put the square 5 on the two to eliminate the 5 on the other side?

take the 5th root of both sides and continue
• Oct 26th 2008, 12:17 PM
dc52789
Quote:

Originally Posted by Jhevon
take the 5th root of both sides and continue

is it 0.149 => 15%?
• Oct 26th 2008, 12:20 PM
Jhevon
Quote:

Originally Posted by dc52789
is it 0.149 => 15%?

yeah, around 14.9%