These are finance questions I am working on and need help with. Please and thank you!

1. Your neighbor has just won the state lottery and has three award options to choose from. He can elect to receive a lump-sum payment today of $20 million, 5 annual end-of-year payments of $4.75 million, or 15 annual end-of-year payments of $2.0 million.

a) If he expects to earn a 7 percent annual return on his investments, calculate the present value of each of the three options. For the 5-year stream of payments, you must use the step-by-step method to calculate the present value. Be sure to show all your work. For the 15-year stream of payments, you may use your financial calculator. Given your results, which option should he choose and why?

b) Using your financial calculator, what is the minimum annual payment your neighbor must receive to be indifferent between the $20 million lump sum payment and the 15-year annuity?

2. Two bonds make semiannual interest payments of $50. Bond A matures in 2 years and Bond B matures in 12 years. Both bonds currently sell at par ($1,000).

a) Calculate the price of each bond if the yield to maturity increases to 12 percent. What is the percentage change in price for each bond?

b) Calculate the price of each bond if the yield to maturity decreases to 8 percent. What is the percentage change in price for each bond versus the base case?

c) What do you conclude about the relationship between time to maturity and the sensitivity of bond prices to interest rates?

3. An investor has two bonds in his portfolio. Each bond matures in 10 years, has a face value of $1,000, and has a yield to maturity equal to 5 percent. One bond, Bond C, pays an annual coupon of 9%, the other bond, Bond Y, pays an annual coupon of 1%.

a) Assuming that the yield to maturity of each bond remains at 5 percent over the next 10 years, what will be the price of each bond at each of the following time periods: t=10, t=8, t=6, t=4, t=2, t=0 (t = # of years to maturity)?

b) Plot the time path of the prices for each of the two bonds (x-axis = years to maturity; y-axis = bond value)

4. Bond J is a 3 percent coupon bond. Bond K is an 11 percent coupon bond. Both bonds have 9 years to maturity, make semiannual payments, and have a yield to maturity of 7 percent. Suppose interest rates decrease from 7 percent to 5 percent. Calculate which bond will experience the greater percentage increase in price. Explain the relationship between coupon rate and the sensitivity of bond prices to interest rates.