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

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Question 1006877: 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 $1000 to grow to $1092.03 in 2 years? Round your answer to the nearest tenth of a percent if needed.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the formula is A = P * (1+r)^2

P = 1000
r = the annual interest rate
A = 1092.03

the formula becomes:

1092.03 = 1000 * (1+r)^2

divide both sides of this equation by 1000 to get:

1092.03 / 1000 = (1+r)^2

raise both sides of that equation to the power of 1/2 to get:

(1092.03 / 1000) ^ (1/2) = 1 + r

the expression on the right side of the equation becomes 1 + r because:

((1+r)^2)^(1/2) becomes (1+r)^(2 * 1/2) which becomes (1+r)^1 which becomes 1+r.

subtract 1 from both sides of this equation to get:

(1092.03 / 1000) ^ (1/2) - 1 = r

solve for r to get:

r = .045002392

confirm by replacing r in the original equation with .045002392 to get:

1092.03 = 1000 * (1.045002392)^2 which becomes:

1092.03 = 1092.03, confirming the solution is correct.
1.

your solution is r = .045002392

the percent is 100 * .045002392 = 4.5002392%.

round that to the nearest tenth of a percent and your solution becomes:

r = 4.5%.