3.Mr. D. plans to retire exactly twenty years from now (t=0), and he would like to have accumulated, by retirement, enough money to enjoy a $100,000 per year retirement income beginning in year 21 and continuing in perpetuity thereafter. So far he has saved up $50,000, all in stocks (that is, at t=0 his pension account contains $50,000).

a) What must his annual contributions be if he is to achieve his goal (assume he makes 20 payments)? On average he expects to earn 10% on his money.

b) The stock market collapses. By the end of the day (it is still t=0)his accumulated wealth has fallen to $30,000. Assuming he still expects on average to earn 10%, how much must he now contribute (assume 20 equal payments)?