Question 1023549
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.