SOLUTION: How long will it take for any amount of money to triple if invested at 6% annual interest and compounded quarterly and compounded monthly. I set it up 3=1(1+(.06/4)^4t
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Question 541872: How long will it take for any amount of money to triple if invested at 6% annual interest and compounded quarterly and compounded monthly. I set it up 3=1(1+(.06/4)^4t
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Ok, that is the correct set up for the 'compounded quarterly' scenario.
^{4t}\ =\ 3)
Do the indicated arithmetic and then take the log of both sides (any base, doesn't matter)
^{4t}\ =\ \ln(3))
Use
\ =\ n\log_b(x))
to write:
\ =\ \ln(3))
Then a little straight-up algebra:
}{4\,\cdot\,\ln(1.015)})
The monthly one works out the same way except that you start with:
^{12t}\ =\ 3)
And end up with
}{12\,\cdot\,\ln(1.005)})
Both of them are 18+ years, but the more frequent compounding gets you to your goal about 30 days earlier.
The reason that the logarithm base doesn't matter is that
}{\ln(\beta)}\ =\ \frac{\log(\alpha)}{\log(\beta)}\ =\ \frac{\log_b(\alpha)}{\log_b(\beta)})
for all real 
and 
John
My calculator said it, I believe it, that settles it
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