To find out how long it takes for $1,000 to quadruple in value with an 11% annual return, we can use the compound interest formula:
Future Value = Present Value * (1 + Interest Rate)^Time
In this case, we want to find the time it takes for the Future Value to be four times the Present Value:
$4,000 = $1,000 * (1 + 0.11)^Time
Dividing both sides of the equation by $1,000, we get:
4 = (1.11)^Time
Taking the logarithm of both sides (base 1.11), we have:
log base 1.11 (4) = Time
Using a calculator, we find that log base 1.11 (4) is approximately 7.116.
Therefore, it takes approximately 7.116 years for $1,000 to quadruple in value with an 11% annual return when compounded annually.