We can use the formula for simple interest to solve this problem:
Simple Interest = Principal * Rate * Time
Where:
Principal = $900
Rate = 4% = 0.04
Simple Interest = $1800 - $900 = $900
Substituting these values into the formula and solving for time:
$900 = $900 * 0.04 * Time
Time = $900 / ($900 * 0.04) = 25 years
Therefore, it will take 25 years for the value of the account to reach $1800 with a 4% simple interest rate.