Please Show work!

A) A few years from now you have decided you want to purchase your first home. Youve saved up a $20,000 down payment. The house you want to buy costs $350,000. If interest rates are 5% for a 30 year mortgage, how much will your monthly payment be? What if you could get a 4% loan?

B) A few years from now you have decided you want to purchase your a home. Youve been budgeting for a while and you know you can afford a mortgage payment of $1,000/month. You checked with the bank and found out mortgage rates are 5% for a 30 year mortgage. How much will you be able to borrow?

Remember keep rate in sync with time: 5%/yr = .4167%/month

C) In 40 years you are ready to retire. Youve saved well over the course of your career and you have $500,000 in your 401K. Youre tired of the fluctuations in the market and youd rather just convert your 401K to an annuity and receive a guaranteed fixed payment for your final 20 years. If you give the insurance co. the full $500K in return for their promise to pay $75,000 per year, what interest rate is implied?

D) You plan to save $15,000 a year for 40 years until you retire. If you earn 7% on your money, how much will you have when you retire?