Multiple choice

Emma deposited x dollars at an annual interest rate of 6%, compounded annually. After one year, she deposited another x dollars into the same account. If the total amount in her account after two years was y dollars, then which of the following expresses x in terms of y?

  1. y 1 + 1.06

  2. y 1.06 + 1.12

  3. y 1.06 + 1.18

  4. y 1.06 + (1.06) 2

  5. y (1.06) 2 + (1.06) 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After one year, the first deposit x grows to x(1.06). Then another x is added, making the total x(1.06) + x. After the second year, this entire amount grows by 6%, resulting in (x(1.06) + x)(1.06) = x(1.06)^2 + x(1.06) = y. Factoring out x gives x(1.06 + 1.06^2) = y, so x = y / (1.06 + 1.06^2).

AI explanation

The first deposit of x dollars compounds for two years, growing to x times 1.06 squared, and the second deposit of x dollars compounds for one year, growing to x times 1.06. The total amount y is the sum of these values, so y equals x times 1.1236 plus x times 1.06. Factoring out x gives y equals x times 2.1836, meaning x equals y divided by 2.1836. This corresponds algebraically to the expression y divided by the sum of 1.06 and 1.06 squared.

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