SATMathematics Practice Test 1

The initial deposit earns 2 percent interest compounded annually.
Thus at the end of 1 year, the new value of the account is the initial deposit of 100 plus 2 percent of the initial deposit: $100+\frac{2}{100}\left(100\right)=100\left(1.02\right)$.
Since the interest is compounded annually, the value at the end of each succeeding year is the sum of the previous year’s value plus 2 percent of the previous year’s value.
This is again equivalent to multiplying the previous year’s value by 1.02.
Thus, after 2 years, the value will be $100\left(1.02\right)\left(1.02\right)=100{\left(1.02\right)}^2$ after 3 years, the value will be $100{\left(1.02\right)}^3$; and after t years, the value will be $100{\left(1.02\right)}^{\mathit{t}}$.
Therefore, in the formula for the value for Jessica’s account after t years, $100{\left(\mathit{x}\right)}^{\mathit{t}}$, the value of $\mathit{x}$ must be 1.02.