1. **Stating the problem:** We need to determine in which scenario compound interest is more beneficial than simple interest. 2. **Understanding the concepts:** - Simple interest is calculated only on the principal amount using the formula $$SI = P \times r \times t$$ where $P$ is principal, $r$ is rate, and $t$ is time. - Compound interest is calculated on the principal plus accumulated interest using the formula $$CI = P \left(1 + r\right)^t - P$$. 3. **Key rule:** Compound interest grows faster than simple interest over time because interest is earned on interest. 4. **Analyzing each scenario:** - a. Short-term loan: Since time $t$ is small, compound interest advantage is minimal. - b. Investment reinvested for several years: Over multiple years, compound interest accumulates significantly more than simple interest. - c. Loan with no interest: Neither simple nor compound interest applies. - d. Interest-only loan: Interest is paid periodically without reinvestment, so compound interest does not apply. 5. **Conclusion:** Compound interest is more beneficial in scenario **b. An investment reinvested for several years** because the interest earned is reinvested and grows exponentially over time. **Final answer:** Scenario b