Question

At the end of 2​ years, P dollars invested at an interest rate r compounded annually increases to an​ amount, A​ dollars, given by the following formula. find the interest rate $128 increased to$ 242 in 2 years.

Write your answer as a percent
With the formula A=P(1+r)^2

Answer 1

the interest rate is 37.5%.

Explanation:

To find the interest rate (r) when $128 increases to $242 in 2 years using the formula A = P(1 + r)^2, we can set up the equation as follows:

$242 = $128(1 + r)^2

Now, let's solve for r:

Divide both sides by $128:

(1 + r)^2 = $242 / $128

(1 + r)^2 = 1.890625

Take the square root of both sides to solve for 1 + r:

1 + r = √(1.890625)

1 + r = 1.375

Now, subtract 1 from both sides to find r:

r = 1.375 - 1

r = 0.375

To express the interest rate as a percentage, multiply by 100:

r = 0.375 * 100 = 37.5%