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!



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



cool cool cool

 Dec 1, 2017

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