Asked by Ariana Montgomery on Mar 10, 2024

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The amount A in an account earning r percent (in decimal form) compounded annually for two years is given by $A=P(1+r)_{2}$ where P is the original investment. What is the interest rate r , as a percent, if the amount in the account is $235.44 and the original investment was $208 ? Round your answer to two decimal places.

A) 5.89 %

B) 6.89 %

C) 6.39 %

D) 5.39 %

E) 7.39 %

A) 5.89 %

B) 6.89 %

C) 6.39 %

D) 5.39 %

E) 7.39 %

Compounded Annually

Refers to the process of calculating and adding interest to the principal balance of an investment or loan once per year.

Investment

Allocation of resources, usually money, in the expectation of generating an income or profit.

Interest Rate

The ratio of a quantity of money that is charged for its use, usually represented as a yearly percentage rate.

- Understand and apply the formula for compound interest to solve problems.

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Mar 10, 2024

Final Answer :

C

Explanation :

First, we need to solve for the interest rate, r:

$235.44 = $208(1+r)^2

Dividing both sides by $208:

1.13 = (1+r)^2

Taking the square root of both sides:

1.06 = 1+r

Subtracting 1 from both sides:

r = 0.06 = 6%

Therefore, the interest rate is 6%, which corresponds to answer choice C when rounded to two decimal places.

$235.44 = $208(1+r)^2

Dividing both sides by $208:

1.13 = (1+r)^2

Taking the square root of both sides:

1.06 = 1+r

Subtracting 1 from both sides:

r = 0.06 = 6%

Therefore, the interest rate is 6%, which corresponds to answer choice C when rounded to two decimal places.

## Learning Objectives

- Understand and apply the formula for compound interest to solve problems.