Question: Social Security and Compound interests

Interest rate is 4% per year. Would you accept a proposal to pay $10,000 for one year and will be paid back $15,000 in the following year?

1. Will you accept the proposal to pay $10,000 for ten years and then will be paid back $15,000 per year for the following ten years?

2. Will you accept the proposal to pay $10,000 for twenty years starting at age 42, and starting from age 62 will be paid back $15,000 per year for the following twenty years?

3. If you are 52 now, will you accept the proposal to pay $10,000 for ten years starting now, and starting from age 62 will be paid back $15,000 per year for the following twenty years?

4. How old is the person whose social security account will break even?

5. How does your answer change if interest rate is 3%? (This question examines how sensitive your answer will be as interest rate changes.)

Notes: Compound interest present value

(1.04) 1/(1.04) = 0.96

(1.04)² = 1.08 1/(1.04)² 0.92

(1.04)¹⁰ = 1.48 1/(1.04)¹⁰ 0.67

(1.04)²⁰ = 2.2 1/(1.04)²⁰ 0.45