A person living in an apartment puts down a $300 deposit when they move in and then pays $700 of rent each month for a year

To calculate the total amount paid for rent throughout the year:

$700 per month x 12 months = $<<700*12=8400>>8,400

Adding the initial deposit:

$8,400 + $300 = $<<8400+300=8700>>8,700

Therefore, the person paid a total of $8,700 for rent throughout the year, including the initial deposit.