Question 1025819
I am stuck at this step: $4000 = $3000 * (1+r)^3.


divide both sides of this equation by 3000 to get:


4000/3000 = (1+r)^3


take the third root of both sides of this equation to get:


(4/3)^(1/3) = 1+r


subtract 1 from both sides of this equation to get:


(4/3)^(1/3) - 1 = r


solve for r to get:


r = .1006424163.


multiply by 100 to get r = 10.06424163%.


round to the nearest tenth to get r = 10.1%


HOWEVER, .....


this would not be correct.


you needed to use the continuous compounding formula.


that formula is f = p * e^(nr)


f = future value
p = present value
e = scientific constant of 2.71828...
n = number of time periods.
r = interest rate per time period.


that formula would get you:


4000 = 3000 * e^(3r)


divide both sides of this equation by 3000 to get:


4000/3000 = e^(3r)


simplify to get:


4/3 = e^(3r)


take the natural log of both sides of this equation to get:


ln(4/3) = ln(e^(3r))


since ln(e^(3r)) is equal to 3r*ln(e), and since ln(e) = 1, then the equation becomes:


ln(4/3) = 3r


divide both sides of the equation by 3 to get:


ln(4/3)/3 = r


solve for r to get:


r = .0958940242


multiply by 100 to get r = 9.58940242%.


round to the nearest tenth to get r = 9.6%.


you needed the continuous compounding formula because the problem stated if interest is compounded continuously.