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# Kimberly borrows dollars from Lucy, who charged interest of per month (which compounds monthly). What is the least integer number of

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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

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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

Dec 1, 2017