Homework

HOMEWORK SETS

Part 1: Basic Concepts

1.

a. How long will it take to double your money with an interest rate of 10 percent? 20 percent? 40 percent? What about tenfold increase in your money with a growth rate of 50 percent?

b. On the advice of your broker ten years ago, you invested in a $6 stock that is now selling for $30. At what rate has your capital grown?

c. Your father is about to retire. His firm has given him the option of retiring with a lump sum of $50,000 or an annuity of $8,000 for ten years. Which is worth more now, if the discount rate is (1) 6%, (2) 18%?

d. You are offered a $15,000 life insurance policy requiring thirty annual payments of $195 each. What is the compound value of the payments that you will have made after the policy is paid up, assuming that the discount rate is 10 percent?

2. Suppose that in period t = 1, two states of the world can occur, state Good (G1) and Bad (B1)each with probability.5. Similarly in date t 2 there are also two possible states - Good(G2) and Bad (B2) with probabilities .4 and .6 respectively, independent of what state is realized in period 1. The following securities are priced:

|Price | |Payoff | | | |

|$.45 |$1 | if state G1 |at t=1 | occurs, |$0 otherwise |

|$.45 |$1 |if state B1 |at t=1 |occurs, |$0 otherwise |

|$.30 |$1 |if state G2 |at t=2 |occurs, |$0 otherwise |

|$.50 |$1 |if state B2 |at t=2 |occurs, |$0 otherwise |

What should be the price of a risk-free coupon bond that pays 5% (5% coupon) and comes due at year 2 (face value of $1,000)....