Compound Interest

Question

$1000 invested at 3% for 2 years compounded annually=

A=1000(1+.03/1)^2= 1060.90

I completely understand this problem, though this is obviously not my question.

What if I am given:

1060.90= 1000(1+r/1)^2 ...and am asked to find the rate of interest. How do I figure that out given this information?

Answer 1

Just showing each step in case you were unsure of the Algebra used here.

1060.90 = 1000(1+r)²

First, divide both sides by 1000

1060.90 ÷ 1000 = 1000(1+r)² ÷1000

Now you must clear the radical. You can do this by taking the nth root √ on the right side and raising the left side to the 1/nth power. The exponent is 2, so n=2. This will clear the parenthesis as well.

1.0609^(1/2) = √(1+r)²

Now subtract one form both sides

1.03 - 1 = r

r = .03

Answer 2

1060.90 = 1000(1 + r)²

1.0609 = (1 + r)²

1.03 = 1 + r

0.03 = r