Shota invests $1000 in a certificate of deposit that earns interest. The investment's value is multiplied by 1.02 each year. Which expression gives the investment's value after 5 years? Choose 1 answer: (A) 1000*1.02^(5) (B) 1000*(1+1.02)^(5) (C) 1000+(1+1.02)^(5) (D) 1000+1.02^(5)

Question

Shota invests  $1000 in a certificate of deposit that earns interest. The investment's value is multiplied by 1.02 each year. Which expression gives the investment's value after 5 years? Choose 1 answer: (A)  1000*1.02^(5) (B)  1000*(1+1.02)^(5) (C)  1000+(1+1.02)^(5) (D)  1000+1.02^(5)

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to find the expression that represents the value of an investment after 5 years, given that the investment increases by a factor of 1.02 each year.Identify the correct formula: Identify the correct formula for compound interest. The value of an investment that earns compound interest is calculated using the formula: Final Value = Initial Investment * (1 + Interest Rate)^(Number of Periods) In this case, the interest rate is 2% or 0.02, and the number of periods is 5 years.Translate the information: Translate the information into the formula. Using the formula from Step 2, we can write the expression for the investment's value after 5 years as: Final Value = 1000 * (1 + 0.02)^(5) Simplify the expression inside the parentheses: Final Value = 1000 * (1.02)^(5)Match the expression with the given options: Match the expression with the given options. The expression we found in Step 3 is 1000 * (1.02)^(5), which corresponds to option (A).

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