SOLUTION: 13. An amount of $2000 earns $400 interest in 3 years and 2 months. What is the effective annual rate of interest compounds monthly?

Question 1141245: 13. An amount of $2000 earns $400 interest in 3 years and 2 months. What is the effective annual rate of interest compounds monthly?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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%.

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