1. **State the problem:** Find the principal amount that will grow to a future value of 4116.00 at a simple interest rate of 8.7% over 4 months. 2. **Formula for simple interest:** $$ A = P(1 + rt) $$ where $A$ is the future value, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Convert time to years:** Since 4 months = $\frac{4}{12} = 0.333333$ years. 4. **Plug in known values:** $$ 4116 = P(1 + 0.087 \times 0.333333) $$ 5. **Calculate the interest factor:** $$ 1 + 0.087 \times 0.333333 = 1 + 0.028999 = 1.028999 $$ 6. **Solve for $P$:** $$ P = \frac{4116}{1.028999} $$ 7. **Show cancellation step:** $$ P = \frac{4116}{\cancel{1.028999}} \times \cancel{\frac{1}{1.028999}} $$ 8. **Calculate $P$:** $$ P = 4000.000 $$ **Final answer:** The principal is 4000.00.