Final answer:
The correct formula for calculating the future value of $100 invested at 5% interest for one year is FV = 100 x (1 + 0.05), which is option (a).
Step-by-step explanation:
The formula that illustrates the value of $100 invested for one year at 5% interest is FV = 100 x (1 + 0.05). When applying the simple interest formula, we determine the interest earned by multiplying the principal amount ($100) by the interest rate (0.05) and the time period (1 year), which yields $5 interest. To find the total future value (FV), we then add the interest to the principal amount, giving us FV = 100 + (100 x 0.05 x 1), which simplifies to FV = 100 x (1 + 0.05). Hence, the correct answer is option (a).