Please show all work

6. What should a zero coupon bond maturing for $1000 in 9 years with a 7% market rate sell for? 7. Compute the expected return for the following investment State of nature Probability Return Boom 25% 20% Average 60% 8% Recession 15% 0% 8. The following are the expected returns on a portfolio of investments. What is the expected rate of return on the portfolio? Investment # of shares Price per share Expected return A. 2000 $20 10% B. 3000 $10 15% C. 1000 $15 8% 9. You take out a $200,000 mortgage for 20 years at 6%. 10. What is your monthly payment? 11. What is the principle and interest on the first payment? 12. What is the principle and interest on the twelfth payment? 13. How much interest will you pay over the 20 years? 14. You bought a house 8 years ago with a $250,000 mortgage. It was a 15 year loan with monthly payments which will pay off the loan when you make the last payment. The interest rate was 6%.What are your monthly payment and your current loan balance? How much interest will you pay in the upcoming year? 15. You want to retire has a millionaire. How much do you need to put away each month if: 16. You use common stocks and have an average return of 10%? 17. You use corporate bonds and have an average return of 6%? 18. You use government bonds and have an average return of 4%? 19. You put your money in a CD at 2.5% interest rate? (Please use your own age. If you are over 45, please solve for saving a $100,000.) 20. You are offered a contract with a signing bonus. If they offered you either $215,000 in cash or $2,000 a month for 15 years, guaranteed, which do you take (based strictly on the math)? Your safe rate of return is 7.5%. 21. You are 30 years old today and planning to retire at age 62.You want to plan your finances for living 35 years past age 62 and die dead broke. You determine you will need $3000 per month from age 62 for the 35 years. 22. Your plan is to go live in the tropics, on the beach, and live on coconuts and fishing. Also, you need to conclude your retirement savings at age 55 because all your spare money then will be going to your childrens education. 23. The question is how much money you will need to save each month between now and 55 so that you can quit contributing. The expected return on your investments over the whole period is 10% per year. Please ignore inflation.