Question 606820: I HAVE NO IDEA!!! HELP ME PLEASE! THANKS!!
$2000 dollars was invested into the account at 3% for 5 years. How long will it take for the amount to triple if t is compounded continuously?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I did one very similar to this earlier today. You should be able to figure this one out from the work I showed in that problem, the only substative difference is that you want to triple rather than double. You are probably clever enough to figure out where to put a 3 instead of a 2 -- see below:
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Where  is the future value,  is the present value, i.e. the initial investment,  is the base of the natural logarithms which is the limit of ^n) as  becomes large,  is the annual interest rate expressed as a decimal, and  is the number of years.
Regardless of the amount of the initial investment, in order for it to double,  and therefore  must equal 2.
Hence:
and solve for
Take the natural log of both sides. Actually, the log of any base will work and, given correct arithmetic, will provide the correct answer. However, since the equation involves , the arithmetic is greatly simplified by using the natural log.
\ =\ \ln(2))
Use
\ =\ n\,\cdot\,\log_b(a))
To write
\ =\ \ln(2))
Then use
\ =\ 1)
to write
)
and finally
}{r})
Just use your calculator to divide ) by the interest rate. Don't forget that the interest rate must be expressed as a decimal.
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After that, toss the following into your financial formulas toolkit:
An initial investment of at an interest rate of compounded continuously will increase by a factor of  in }{r}) years.
John
My calculator said it, I believe it, that settles it
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