Problem 1 (10 points):

You have decided to buy a perpetuity. The bond makes one payment at the end of every year forever and has an interest rate of 10%. If you initially put $1000 into the bond, what is the payment every year?

Problem 2 (40 points):

You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 8 years. You expect that the drugs profits will be $2 million in its first year and that this amount will grow at a rate of 2% per year for the next 8 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 5% per year?

Exercise 3 (30 points):

You are thinking of purchasing a house. The house costs $280,000. You have $20,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 20-year mortgage that requires annual payments and has an interest rate of 5% per year. What will your annual payment be if you sign up for this mortgage?

Exercise 4 (13 points): Theoretical question (150 words maximum)

Explain with your own words (no textbook definitions needed) what is annuity? Give 2-3 examples from finance where we can use annuity formula for the valuation of cash flows.

Exercise 5* (7 points):

Using the concept of geometric series, derive the formula of present value of perpetuity.