Which formula illustrates the value of \$100 invested for one year at 5 percent interest?

• A. \$100 \times 0.05$
• B. \$100 \div (1 + 0.05)$
• C. \$100 + (100 \times 0.5)$
• D. \$100 \times (1 + 0.05)$

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the concept of simple interest. Simple interest is calculated by multiplying the principal amount (initial investment) by the interest rate and the time period. In this case, the principal is \$100, the interest rate is 5% (or 0.05), and the time period is 1 year.
2. Step 2: Recognize that the formula for the total value of an investment after one year includes both the principal and the interest earned. This is expressed as: Total Value = Principal × (1 + Interest Rate).
3. Step 3: Compare the given formulas to the correct formula for calculating the total value of the investment. The correct formula is \$100 × (1 + 0.05)$, which accounts for both the principal and the interest earned.
4. Step 4: Eliminate incorrect options by analyzing their structure. For example, \$100 × 0.05\( calculates only the interest earned, not the total value. \)100 ÷ (1 + 0.05)\( is not relevant to this scenario, as it suggests a discounting approach. \)100 + (100 × 0.5)$ incorrectly uses 0.5 instead of 0.05 as the interest rate.
5. Step 5: Confirm that the correct formula, \$100 × (1 + 0.05)$, accurately represents the total value of the investment after one year, including both the principal and the interest earned.