42. You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continu- ing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday? 43. You realize that the plan in Problem 42 has a flaw. Because your income will increase over your lifetime, it would be more realistic to save less now and more later. Instead of putting the same amount aside each year, you decide to let the amount that you set aside grow by 3% per year. Under this plan, how much will you put into the account today? (Recall that make the first contribution to the account today.) you are planning to C (1.03) 35 1.03 PV= 1- +C. 0.05 0.03 1.05 The PV of $2 million in 35 years is: 2,000,000 (1.05) 35 =$362,580.57. Setting these equal gives: C (1.03) 35 1.03 +C =362,580.57. 0.05 -0.03 1.05 The present value of a growing annuity is 1 g CXL (1-(+)" ) Cx r-g