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!


1+0 Answers



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

CPhill  Dec 1, 2017

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