Present value questions

1. A government bond pays $100 in coupons per year starting in one year for 8 years, and $1000 principal along with the last coupon. If the discount rate is 4% per year, what is the value of the bond today? 2. A homeowner wishes to borrow $500,000, but must repay interest and principal with monthly flat payments over 30 years. If the simple annual interest rate is 6%, i.e. the monthly rate is 0.5%, what is the monthly payment? What is the remaining balance (amount owed) after five years of payments? 3. Suppose a bank wanted to offer the borrower in #2 an option to have the payments grow at 1% a month for the full 30 year period. What would the initial payment be in this case, in order to have the same present value? 4. A retiree saved $250,000 and wants to withdraw $5000 per month for expenses, starting next month. How many months (n) will the money last if the annual discount rate is 5%? What is the general formula to solve for n as a function of r? Hint: You may need to take a natural log. 5. How does your answer to #4 change if the retiree increase the withdrawal by 0.5% per month