Question

Cathy placed $6000 into a savings account. for how long can $700 be withdraw from the account at the end of every month starting one month from now if interest is 5.67% compounded monthly?

Answer 1

To find out for how long the $700 can be withdrawn from the account every month, we need to use the formula for compound interest. In this case, $700 can be withdrawn from the account at the end of every month for approximately 6.38 months.

Step-by-step explanation:

To find out for how long the $700 can be withdrawn from the account every month, we need to use the formula for compound interest.

The formula for compound interest is: A = P(1 + r/n)^(nt)

Where:

• A is the amount of money accumulated after n years, including interest
• P is the principal amount (the initial deposit)
• r is the annual interest rate (written as a decimal)
• n is the number of times that interest is compounded per year
• t is the number of years

In this case, we know that the principal amount is $6000 and the interest rate is 5.67% compounded monthly. We also know that $700 will be withdrawn at the end of every month. So we need to find out for how long the $700 withdrawals will not deplete the account.

We can rearrange the formula to solve for t:

t = (log(A/P))/(n * log(1 + r/n))

Substituting the given values:

t = (log(6000/700))/(12 * log(1 + 5.67/100)) = 6.38 months

Therefore, $700 can be withdrawn from the account at the end of every month for approximately 6.38 months.