John Smith's current age is 60 with a net worth of $40 million, he is thinking about her retirement. He expects to retire fully in 10 years when he turns 70. He expects that his income will exactly offset his spending until his retirement. John is considering three different ways to reinvest his $40 million net worth to maximize his net worth at retirement. The options are:

1. Invest his entire current net worth in 10-year coupon bonds with coupon rate 5% making semiannual coupons. These bonds have face value of $10,000 and are currently selling at $9,920. The coupon payments can be reinvested in John's retirement account earning 6.5% annual effective rate. Assume that it is possible to purchase a fraction of a bond.

2. Invest his entire current net worth in an annuity that pays an increasing monthly payment for the next 10 years (a total of 120 payments), with the first payment of $180,000 a month from now. Each subsequent payment is $4,000 higher than the previous payment. The annuity payments are then being reinvested in John's retirement account earning 6.5% annual effective rate.

3. Invest half of his net worth in 10-year coupon bonds as described in (option 1) and the other half in the annuity as described in (option 2). Since he is investing half as much in the annuity, all the monthly payments are exactly half of what is described in (option 2). Upon retirement, he wishes to continue his current lavish lifestyle. His current annual spending is $2.5 million. The inflation rate is projected to be 3.7% on average within his lifespan. In order to facilitate his retirement withdrawals, he will put his accumulated net worth at the time he retires (basically everything that he has accumulated at that time) into his retirement account that gives an annual effective return of 6.5%. he plans to then withdraw annually the amount that is equivalent to his $2.5 million annual spending now, with the first withdrawal at the beginning of his retirement right when he turns 70. he also expects to live until the age of 95 (therefore, his last withdrawal should be right when he turns 94, there is no point of withdrawing when he turns 95 since he predicts that he will die immediately after).

1. What will be the amount that John Smith withdraws when he turns 85? How much does he need to have in his retirement account at the time when he retires in order to maintain the same amount of annual spending (inflation adjusted)?

2. Based on the investment option (1) described above, how many coupon bonds can John purchase using his net worth today? What is the amount that he will have in his retirement account at the time he retires as he turns 70? What is the effective annual return of investment option (1) based on the accumulated amount at age 70 and his current net worth?

3. Calculate the annual effective return of the annuity described in investment option (2) not taking into account the possibility of reinvestment of the payments from the annuity (based only on the initial investment and the annuity payments). What is the amount that John will have in his retirement account at the time he retires as he turns 70 if he chose option (2)? What is the effective annual return of investment option (2) based on the accumulated amount at age 70 and his current net worth?

4. If John chose investment option (3), how many coupon bonds will he purchase? What is the amount that John will have in his retirement account at the time he retires as he turns 70 if he chose option (3)? What is the realized effective annual return of investment option (3)?

5. Which investment option can allow John to continue his current lifestyle beyond retirement? Which investment option gives the highest realized effective annual return?