SOLUTION: The formula A=P(1+r)^2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r (where r is given as a decimal), using compound interest. What intere

Question 1065333: The formula A=P(1+r)^2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r (where r is given as a decimal), using compound interest. What interest rate will cause $3000 to grow to $3307.50 in 2 years?
The interest rate is ___ %
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula is A = P * (1 + r)^2.

if you let P = 3000 and you let A = 3307.50, then the formula becomes:

3307.50 = 3000 * (1 + r)^2

divide both sides of the equation by 3300 and you get:

3307.50 / 3000 = (1 +r)^2

take the square root of both sides of this equation and you get:

(3307.50 / 3000)^(1/2) = 1 + r

subtract 1 from both sides of this equation to get:

(3307.50 / 3000)^(1/2) - 1 = r

solve for r to get:

r = .05

replace r in your original equation by .05 and you get:

3307.5 = 3000 * (1.05)^2

evaluate this equation to get 3307.5 = 3307.5

r = .05 is your solution.
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