+1452 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?
Thanks so much!
+129918
Note that the time to double the money is independent of the amount borrowed.....thus.... it takes as long for $1 to double as it does for $1000 to double [ believe it, or not !!!]
So calling the original amount, A..... we have that
2A = A (1.05)^N where N is in months.....divide both sides by A
2 = (1.05)^N take the log of both sides
log 2 = log (1.05)^N and by a log property, we can write
log 2 = N * log (1.05) divide both sides by log (1.05)
log (2) / log (1.05) = N ≈ 14.2 months
And the least integer greater or equal to 14.2 = 15
