Final answer:
To find out how long $900 can be withdrawn from the account at the end of every month, we need to calculate the future value of the $7000 principal using compound interest. By substituting the values into the formula and solving for time, we find that $900 can be withdrawn for approximately 3 years and 9 months.
Step-by-step explanation:
To find out how long $900 can be withdrawn from the account at the end of every month, we need to calculate the future value of the $7000 principal. We can use the formula for compound interest:
Future Value = Principal × (1 + Interest Rate)^Time
In this case, the principal is $7000, the interest rate is 5.02% (converted to decimal form: 0.0502), and we need to solve for the time. The future value is the accumulated amount in the account after the desired number of months. Let's substitute in the values and solve for time:
$900 = $7000 × (1 + 0.0502)^Time
Dividing both sides by $7000 gives:
1.28 = (1.0502)^Time
Taking the logarithm of both sides gives:
Time = log(1.28) / log(1.0502)
Using a calculator, we find that the approximate time needed is 45.5 months or about 3 years and 9 months. Therefore, $900 can be withdrawn from the account for approximately 3 years and 9 months if $7000 is initially deposited.