1. You invested $1,400 in an account that pays 5 percent simple interest. How much more could you have earned over a 20-year period if the interest had compounded annually? 2. In 1895, the winner of a competition was paid $150. In 2006, the winner's prize was $70,000. What will the winner's prize be in 2040 if the prize continues increasing at the same rate? 3. Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $100. However, once built the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $1000 to build. Your buddy wants to know if he should invest the money to construct it. a. If the interest rate is 9.5% per year, what should your buddy do? b. How would your answer change if the machine takes one year to build? 4. You are shopping for a car and read the following advertisement in the newspaper: "Own a new Spitfire! No money down. Four annual payments of just $10,000." You have shopped around and know that you can buy a Spitfire for cash for $32,500. What is the interest rate the dealer is advertising (what is the IRR of the loan in the advertisement)? Assume that you must make the annual payments at the end of each year. 5. You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug's profits will be $2 million in its first year and that this amount will grow at a rate of 5% per year for the next 17 years. Once the patent expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 10% per year? 6. Your bank account pays interest with an EAR of 5%. What is the APR quote for this account based on semiannual compounding? What is the APR with monthly compounding? With smaller compounding period but a constant EAR, how does the APR change? For advertisement purposes which period would you use: annual, semi-annual, monthly, or daily? 7. Capital One is advertising a 60-month, 5.99% APR motorcycle loan. If you need to borrow $8000 to purchase your dream Harley Davidson, what will your monthly payment be? 8. You are scheduled to receive annual payments of $5,100 for each of the next 7 years. The discount rate is 10 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?