It appears that the question is somewhat related to investments and insurance policies and not directly about the math scenario you mentioned earlier. However, to answer this new question about which product S should purchase for greater gains than bonds with protection of the principal and low risk:
Equity Index Insurance would be the most appropriate choice. This type of insurance typically offers the potential for higher returns linked to the performance of a market index, like the S&P 500, while also providing a guarantee of the principal amount. This means that even if the index performs poorly, the principal amount that S invests will not be lost, thus offering a blend of growth potential with safety.
1. Equity Index Insurance: Provides the possibility of earning higher returns linked to a stock market index. Importantly, it also protects the principal amount, meaning the initial investment cannot decrease in value.
2. Endowment: Primarily used for savings where it pays a lump sum on maturity or on death. It doesn't typically offer returns higher than bonds and isn't primarily focused on protecting the initial principal in terms of market-linked gains.
3. Graded Whole Life Policy: A type of life insurance policy that provides a death benefit and accumulates cash value. Returns are generally not as high as equity index insurance since they are designed more for long-term insurance coverage and steady growth.
4. Return of Premium Policy: This is a life insurance policy that returns the premiums paid if the policyholder outlives the term. While it may offer low risk, it does not provide the growth potential associated with equity index insurance.
Therefore, the best recommendation for S would be:
Equity Index Insurance.
