Multiple choice

Jessica opened a bank account that earns $2$ percent interest compounded annually. Her initial deposit was $ $100$, and she uses the expression $ $100{ \left( x \right) }^{ t }$ to find the value of the account after $t$ years. What is the value of $x$ in the expression?

  1. 1.01

  2. 1.02

  3. 1.03

  4. 1.2
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B Correct answer
Explanation

The formula for compound interest is A = P(1 + r/100)^t. Here, P = 100, r = 2, so the expression is 100(1 + 2/100)^t = 100(1.02)^t. Thus, x = 1.02.

AI explanation

For compound interest, the value of the account after t years is given by the formula Amount = Initial Deposit multiplied by (1 + Rate) raised to the power of t. Comparing this to the provided expression 100 multiplied by (x) raised to the power of t, we see that x = 1 + Rate. Substituting the 2 percent interest rate (0.02) gives x = 1.02.

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