You are currently 30 years of age. You intend to retire at age 60 and you want to be able to receive a 20-year, $100,000 beginning-of-year annuity with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday. a. If you expect your investments to earn 12 percent per year over the next 15 years and 10 percent per year thereafter, how much must you accumulate by the time you reach age 45
1. If you expect your investments to earn 12% per year over the next 15 years and 10% per year thereafter, how much must you accumulate by the time you reach age 45?
2. What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming you currently have $10,000 available to meet your goal?

1. consider a two-firm industry. firm 1 (the incumbent) chooses a level of output qı. firm 2 (the potential entrant) observes qı and then chooses its level of output q2. the demand for the product is p 100 q, where q is the total output sold by the two firms which equals qi +q2. assume that the marginal cost of each firm is zero. a) find the subgame perfect equilibrium levels of qi and q2 keeping in mind that firm 1 chooses qi first and firm 2 observes qi and chooses its q2. find the profits of the two firms-n1 and t2- in the subgame perfect equilibrium. how do these numbers differ from the cournot equilibrium? b) for what level of qi would firm 2 be deterred from entering? would a rational firm 1 have an incentive to choose this level of qi? which entry condition does this market have: blockaded, deterred, or accommodated? now suppose that firm 2 has to incur a fixed cost of entry, f> 0. c) for what values of f will entry be blockaded? d) find out the entry deterring level of q, denoted by q1', a expression for firm l's profit, when entry is deterred, as a function of f. for what values of f would firm 1 use an entry deterring strategy?