You are trying to decide how much to save for retirement. Assume you plan to save $ 7 comma 000 per year with the first investment made one year from now. You think you can earn 8.0% per year on your investments and you plan to retire in36 years, immediately after making your last $ 7 comma 000 investment. a. How much will you have in your retirement account on the day you retire? b. If, instead of investing $ 7 comma 000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be? c. If you hope to live for 29 years in retirement, how much can you withdraw every year in retirement (starting one year after retirement) so that you will just exhaust your savings with the 29th withdrawal (assume your savings will continue to earn 8.0% in retirement)? d. If, instead, you decide to withdraw $ 262 comma 000 per year in retirement (again with the first withdrawal one year after retiring), how many years will it take until you exhaust your savings? (Use trial-and-error, a financial calculator: solve for "N", or Excel: function NPER) e. Assuming the most you can afford to save is $ 1 comma 400 per year, but you want to retire with $ 1 comma 000 comma 000 in your investment account, how high of a return do you need to earn on your investments? (Use trial-and-error, a financial calculator: solve for the interest rate, or Excel: function RATE)

2.You would like to buy a house that costs $ 350 comma 000. You have $ 50 comma 000 in cash that you can put down on the house, but you need to borrow the rest of the purchase price. The bank is offering you a 30-year mortgage that requires annual payments and has an interest rate of 7 % per year. You can afford to pay only $ 23 comma 210 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $ 300 comma 000. At the end of the mortgage (in 30 years), you must make a balloon payment; that is, you must repay the remaining balance on the mortgage. How much will be this balloon payment? Hint: The balloon payment will be in addition to the 30th payment.