SOLUTION: What interest rate is needed in order to double an initial investment of $2000 for two years?

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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