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!

AnonymousConfusedGuy
Dec 1, 2017

#1**+1 **

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

CPhill
Dec 1, 2017