Question 1141245
f = p * (1 + r) ^ n
i = f - p
f = p * i


f is the future value
p is the present value
i is the interest
r is the interest rate per time period
n is the number of time periods


f = p + i = 2000 + 400 = 2400
p = 2000
n = 3 years * 12 = 36 months + 2 = 38 months


formula becomes 2400 = 2000 * (1 + r) ^ 38


divide both sides of the equation by 2000 to get 2400 / 2000 = (1 + r) ^ 38


take the 38th root of both sides of the equation to get (2400/2000) ^ (1/38) = 1 + r.


subtract 1 from both sides of the equation to get (2400/2000) ^ (1/38) - 1 = r


solve for r to get r = .0048094642


replace r with that in the original equation to confirms that it works.


original equation becomes 2400 = 2000 * (1 + .0048094642) ^ 38 which becomes 2400 = 2400, confirming the solution is good.


the nominal annual interest rate is .0048094642 * 12 = .0577135707 * 100 = 5.77135707%.


the effective annual interest rate is (1 + .0048094642) ^ 12 = 1.059264955 - 1 = .0592649545 * 100 = 5.92649545%.