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Question 1023549: What interest rate is needed in order to double an initial investment of $2000 for two years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general equation is f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
in this problem, the time period is years.
you have:
f = 2 * p = 4000.
p = 2000
n = 2
r = what you want to find.
the formula becomes 4000 = 2000 * (1 + r) ^ 2
divide both sides of the equation by 2000 and you get 2 = (1 + r) ^ 2
take the square root of both sides of the eqution to get sqrt(2) = 1 + r
subtract 1 from both sides of the equation to get sqrt(2) - 1 = r
that's your solution.
the decimal equivalent rounded to 5 decimal places is .41421 = r.
that's pretty close, but won't be right on because sqrt(2) is not a rational number.
to test it out, you would replace r and evaluate the original formula.
you would get 4000 = 2000 * (1.141421) ^ 2.
after evaluation, you would have 4000 = 3999.97984...
it's close, but no cigar because of the rounding involved.
if you used 4000 = 2000 * (1 + sqrt(2) - 1) ^ 2, then you would be right on.
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