SOLUTION: I'm stuck on the following problem: What annual interest rate compounded annually is required to provide a 21% increase in the initial investment after 2 years. I tried to

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Question 255266: I'm stuck on the following problem:
What annual interest rate compounded annually is required to provide a 21% increase in the initial investment after 2 years.

I tried to use the formula S = P(1 + i) to the n power.
I put 10,000 in for P as the original investment (just made it up), then I put 12,100 as S the total investment showing an increase of 21%. Then I filled in 4 for n because the interest is compounded annually! Then try and solve for i
Not sure if I'm on the right track!!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
looks like you started off ok.

your formula is:

S = P * (1+i)^n

you used 10,000 for P and 1.21 * 10,000 = 12100 for S.

that's correct but not necessary because you could just as easily have used 1 for P and 1.21 for S.

I don't know why you filled in 4 for n.

if compounding is annually, then n should have been 2 to represent 2 years.

using your numbers for S and P, your formula should have become:

12100 = 10000 * (1+x)^2

x is the annual interest rate.

divide both sides of this equation by 10000 to get:

1.21 = (1+x)^2

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

subtract 1 from both sidesof this equation to get:

solve for x to get:

x = .1

looks like you are looking for 10% a year growth compounded annually for 2 years.

to confirm, substitute in your original equation to get:

12100 = 10000 * (1+x)^2 becomes:

12100 = 10000 * (1.1)^2

simplify to get:

12100 = 12100 confirming the answer is good.