2.Mr. P. Pen, of Minnetonka, Minnesota plans to retire on his 65^th birthday.He is celebrating his 55^th birthday today.He wants to have a fixed retirement income of $125,000 a year for 30 years before his retirement ends.He currently has $400,000 invested in a manner that yields 9.5% annual returns and plans to continue to invest in a way the will yield 9.5% annual returns.He plans to start withdrawing for his retirement on the first day of each year.He can afford to save money at the beginning of each month as required to achieve his goals.How much is that for every month?

1.Miss. Polly Myrrh has been hired as a physicist with American String.American String offers all employees the opportunity to participate in their pension savings plan.The company will match up to 7% of her income that she saves in her pension account. (For every dollar Polly saves, the company puts another dollar in her account until Polly saves up to 7% of her income, after that, the company does not put further additional funds in her savings.)Polly expects her income to grow exactly with inflation during her career.Her retirement account is earning an 8% real rate of return. She wants to never spend more than the real interest earnings from her pension account.She expects to leave the remaining balance to her son, Theodor Kaluza Myrrh.If Polly saves 9% of her income, then approximately how many years will she need to work at American String so that her interest income on this retirement account will exactly support her to the same standard of living as her working income?

2. Ina Udable has been quietly preparing for her retirement.Since she turned 21 years old, at the end of each week she has been saving $100.She is now 50.She plans to continue saving at this rate until she is 66 years old.She would like to withdraw $250,000 at the beginning of each year while she is retired.She plans to live until she is 101 years old.At that time, she wants to give a gift of $5,000,000 to her alma mater, Michigan State University, and an additional $2,500,000 to their Marching Band.How much has Ina accumulated at this time (age 50) if she has been earning 9% from her investments?Will Inas final wishes come true at her present savings rate if she continues to earn 9%?Explain why/why not.

3.An insurance company offers customers aged 45 to 65 the opportunity to buy life insurance policies.They cost $11 per month (end of month payments).This company invests these premiums in a diversified portfolio earning 7.5% returns.They guarantee a payment of $2000 upon the death of the person insured.How long does this person need to remain alive, making payments, for the insurance company to profit from this policy?If the person insured were to save their premiums in an account paying 5% interest, how long would it take for this person to have more money in their account than the payoff from dying while insured?

4. Why is it more important to earn a slightly higher return on a portfolio than to make larger deposits over extended periods of time (i.e. 30 or more years)?