1 Annuity Many people prefer traditional pension (defined benefit plans) to 401 (k) (defined contribution plans) because they like the former's certainty of income. But anyone can construct a traditional pension plan with their 401(k) savings. Suppose after saving every month for 40 years in one's 401 (k), one can retire at 65 with $1 million (Buy SPDR or Vanguard 500!). Assume the person has 25 more years to live, find the monthly income (paid at the beginning of every month) if he/she buys an annuity with a 2% annual return. What about the monthly income, if the annuity lasts for 35 years? For your reference, the median private pension monthly payment is about 8770 and social security's average monthly payment in 2020 is about $1,500. From the findings, do you think defined contribution plans are indeed better? If not, why? 2 Payday Loans An online payday loan offered the borrower $100 cash right away, but the borrower needs to write a personal check of $117.64, payable in two weeks. Calculate the loan's APR and EAR. 3 Bond Pricing Department of Treasury auctioned a 20-year bond in August. Its coupon rate was 1.125% and similar bonds yield at 1.213%. What should the price be? 4 Bond Pricing A mortgage-backed security, with face value $1,000 and semi-annual coupon payments, matures in exactly one year from now. It trades at $1,019.85 now. If its coupon rate is 3% and the next coupon payment is 6 months from now, find its yield to maturity. 5 JGB and U.S. Treasuries The 10-year Japanese Government Bond (JGB) yields 0.01%, while U.S. Treasury's similar issuance yields 0.72%. It seems like the investors like the JGB so much that they are willing to accept close-to-zero interests when lending to the Japanese Government. Both the U.S. Treasury Department and the Japanese Government borrow in the currency they print. Why is the case that only the U.S. Treasuries are considered as the risk-free assets