t=4, if the interest rate is 6% per year? Problem 3: [15 points] Mr. X wants to save money to meet three objectives. First, he wants to retire after 30 years, and for the subsequent 25 post-retirement years, he wants to have an income of $20,000 per month, with the first post-retirement income received 30 years and one month from now. Second, he wants to buy a vacation cabin in 10 years at an estimated cost of $375,000. Third, at the end of 25 years of retirement, he wants to have $2 million. He is currently saving $2500 per month and wishes to do so for the next 10 years, till he buys the cabin. He earns 9.6% APR, compounded monthly, from his savings and we can assume that this will be the rate till retirement. However, after retirement the interest rate is 7% EAR. (a) How much money will he need at the time of retirement that is, at the end of 30 years) in order to be able to withdraw $20,000 per month for 25 years and leave a bequest of $2 million? (b) Will he be able to accumulate this amount if he continues to save $2500 per month till retirement? What will be the short-fall? (c) If he saves at the rate of $2500 per month for 10 years till he buys the cabin, what should his monthly savings be for year 11 to 30 in order to fulfill his objectives