To calculate how much money Dan will have after the first month with a monthly interest rate of 5.25%, you can use the formula for calculating the amount of money after interest is applied:
\[ \text{New Amount} = \text{Initial Amount} \times (1 + \text{Interest Rate}) \]
In this case, Dan's initial amount is $1,200, and the interest rate is 5.25% (which is 0.0525 as a decimal).
Now, plugging in the values:
\[ \text{New Amount} = 1200 \times (1 + 0.0525) \]
\[ \text{New Amount} = 1200 \times 1.0525 \]
\[ \text{New Amount} = 1263 \]
After the first month, Dan will have $1,263 in his money market account.