SOLUTION: $5000 compounded continuously at 5.5% will take how long to grow to $11,300?

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Question 381160: $5000 compounded continuously at 5.5% will take how long to grow to $11,300?
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

When compounding continuously, we use the formula:

A=P%2Ae%5E%28r%2At%29

Where A is the accumulated value, P is the principal, r is the rate, and t is the time in years.

So we are given A=11300 r=.055 P=5000

11300=5000%2Ae%5E%28.055%2At%29

11300%2F5000=e%5E%28.055%2At%29

2.26=e%5E%28.055%2At%29

ln%282.26%29=ln%28e%5E%28.055%2At%29%29

ln%282.26%29=.055%2At%2Aln%28e%29

ln%282.26%29=.055%2At%2A1

ln%282.26%29%2F.055=t

t=14.82481479

So it would take right around 14.825 years for the original $5000 to grow to $11300.

I hope this helps!