1.You are thinking of building a new machine that will save you $1000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 2% per year forever.What is the present value of the savings if the interest rate is 5% per year?

2.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?

3.Your oldest daughter is about to start kindergarten at a private school. Tuition is $10,000 per year, payable at the beginning of the school year. You expect to keep your daughter in private school through high school. You expect tuition to increase at a rate of 5% per year over the 13 years of her schooling. What is the present value of the tuition payments if the interest rate is 5% per year? How much would you need to have in the bank now to fund all 13 years of tuition?