Assuming an annual growth rate of r, compounded continuously, the value of an investment will increase from V subscript 0 to V subscript T over how many years? 1 over r open parentheses V subscript T over V subscript 0 minus 1 close parentheses

fraction numerator ln open parentheses V subscript T divided by V subscript 0 close parentheses over denominator r end fraction

fraction numerator ln open parentheses V subscript 0 divided by V subscript T close parentheses over denominator ln open parentheses 1 plus r close parentheses end fraction

fraction numerator ln open parentheses V subscript T divided by V subscript 0 close parentheses over denominator ln open parentheses 1 plus r close parentheses end fraction