What is the approximate annual rate of return if you invest $6,000 today and expect it to grow to $12,000 in 9 years?

To determine the approximate annual rate of return for an investment that grows from $6,000 to $12,000 over a period of 9 years, it's important to understand the concept of compound interest. The formula used to calculate the future value of an investment is given by:

[ FV = PV \times (1 + r)^n ]

Where:

• ( FV ) is the future value of the investment,

• ( PV ) is the present value (initial investment),

• ( r ) is the annual rate of return,

• ( n ) is the number of years the money is invested.

You are seeking the rate ( r ) where the future value will be $12,000, and the present value is $6,000, over 9 years. Rearranging the formula to solve for ( r ) gives us:

[ (1 + r)^n = \frac{FV}{PV} ]

[ (1 + r)^9 = \frac{12,000}{6,000} ]

[ (1 + r)^9 = 2 ]

To find ( r ), you can take the ninth root of both sides:

[ 1 + r = 2^{