Walter B. answered • 07/04/17
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Since the interest is compounded continuously, the appropriate formula is
Future Value (FV) = Present Value (PV) * ert where r is the interest rate and t is the time period or number of years.
In order to solve for t , the time that it will take for $3000 to grow to $9000 with an interest rate of 3%.
First, we divide both sides by the Present Value
(FV/ PV) = ert
next we take the natural log of both sides
ln(FV/ PV) = ln(ert) = rt
ln(FV/ PV)/r = t
ln(9000/3000)/.03 = 73.24
Even with interest continuously compounded, it will take 73.24 or about 73 years and about 3 months for $3000 to grow to $9000!
Walter B.
You are correct!
I had the correct equation with the wrong numbers.
The ratio of the FV to the PV is three.
Take the natural log of 3 and you get 1.0986 ln(3) = 1.0986
Divide that by .03 and you get 36.62 years 1.0986/.03 = 36.62
so your answer of 37 years (rounded) is correct.
does that make sense
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07/04/17
Joey F.
07/04/17