Logarithmic problem help?
How many years will it take for a $50 investment to grow to $100 if it is compounded continuously at a rate of 5%?
Given formula is:
A(t)=P*e^rt
Where P is initial investment, r is rate, t is time.
Update:My bad , It's not really a logarithmic problem . :p
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Verified answer
Just plug in the given numbers and solve for t, time. Also in this formula, percentage is to be used as decimal. 5% = 0.05
100 = 50*e^(0.05t)
e^(0.05t) = 2
Take natural log of both sides
ln(e^(0.05t)) = ln(2)
ln and e are inverse, so they cancel each other out
0.05t = ln(2)
t = ln(2) / 0.05 = 13.863 years