David is 22 years old (at t = 0) and he is planning for his retirement at age 63 (at t = 41). He plans to save $2,000 per year for the next 15 years (t = 1 to t = 15). He wants to have retirement income of $100,000 per year for 20 years, with the first retirement payment starting at t = 41. How much must David save each year from t = 16 to t = 40 in order to achieve his retirement goal? Assume he plans to invest in a diversified stock-and-bond mutual fund that will earn 8 percent per year on average.