jmc

Question

Kimberly borrows 1000 dollars from Lucy, who charged interest of 5% per month (which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed?

Accepted Answer

Since the amount Kimberly owes is multiplied by 1.05 each month, we want the least integer t for which 1.05^t>2. Trying some integer values of t, we find that 15 is the smallest that satisfies this condition.