SOLUTION: How many years, to the nearest year, will it take money to quadruple if it is invested at 20% compounded annually?
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Question 359737: How many years, to the nearest year, will it take money to quadruple if it is invested at 20% compounded annually?
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
8 years.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The formula for the future value of an investment at discretely compounded interest is:
^{mt})
where
represents the future value
represents the initial investment
is the interest rate as a decimal (
)
is the number of compounding periods per interest term (per year for annual interest rate)
and
is the number of terms (years for annual interest rate)
You don't know 
or 
, but you do know that 
and that we can write the original formula as:
^{mt})
Next, fill in the values you know and simplify:
^{t}\ =\ 4)
^{t}\ =\ 4)
Take the log of both sides (base 10 or natural, doesn't matter which)
^{t}\ =\ \ln(4))
Use the laws of logs:
\ =\ \ln(4))
Divide by )
}{\ln(1.2)})
The rest is arithmetic on the calculator.
John
My calculator said it, I believe it, that settles it
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