Final answer:
To find out how many months the lease runs for, subtract the deposit from the total lease cost and then divide the remaining amount by the monthly payment. Round the answer to the nearest whole number.
Step-by-step explanation:
To find out how many months the lease runs for, we need to consider the total lease cost and the monthly payment. The total lease cost is given as $34,575.04. Let's subtract the deposit of $4,324 from this total to find the remaining amount that will be paid in monthly installments: $$34,575.04 - $4,324 = $30,250.04$
Now, we can divide the remaining amount by the monthly payment to determine the number of months the lease runs for: $$30,250.04 / $589 = 51.37$$
Since we cannot have a fractional number of months, we can round the answer to the nearest whole number. Therefore, the lease runs for 51 months.