4. Combinations: a. A bank markets the following product. You take out a loan today and then repay 2,000 for eight years and 3,000 for another eight years (so that there are 16 payments total). If the interest rate is 4%, what is the size of the loan?

b. A construction company issues the following security. It pays 15 for 10 years. After that it pays 10 forever. If the discount rate is 4.5% what is the current market price of this security? What happens to the price of the security if the interest rate increases to 5.5%?

c. A chemical producer decides to issue a security that makes the following payments. It pays 5 for seven years (it pays 5 starting in one year and then makes another six payments of 5 each year). Then the payments start growing at 3.5% each year and continue forever. (i) What is the payment in year 8? (ii) If the discount rate is 7% what is the present value?

d. An auto parts maker is planning ahead. In 10 years, the auto parts maker must make an investment that will cost 700,000. The auto parts maker has 200,000 in capital today and plans to save a fixed amount at the end of each year for 9 years (at the end of years 1 to 9). If the interest rate is 5% what is the amount that has to be saved every year?