At what annual rate would the following have to be invested

At what annual rate would the following have to be invested? $6,821, to grow to $21,692, in 24 years.   Round the answer to two decimal places in percentage form.

Solution

Amount = principal (1 + rate / number of times interest compounds)^{year * number of times interest compounds}

   $21,692 = $6,821 (1 + rate / 1)^{24* 1}

  $21,692 = $6,821 (1 + rate)²⁴

  $21,692 / $6,821 = (1 + rate)²⁴

3.1802 = (1 + rate)²⁴

[3.1802]^1/24 = [(1 + rate)²⁴]^1/24.

   1.04939 = (1 + rate)

   4.94% = rate

So, the annual rate would be 4.94%