To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.
The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).
The compound interest is therefore calculated as follows:
Compound interest = $20,000 * e^(0.158%*24) - $20,000
= $20,000 * e^0.3832 - $20,000
= $20,000 * 1.454 - $20,000
= $4,080 - $20,000
= -$15,920
So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.