Charles is a senior engineer who has worked for 18 years since he graduatedfrom college. Yesterday in the mail, he received a report from the U.S. SocialSecurity Administration. In short, it stated that if he continues to earn at the samerate, social security will provide him with the following estimated monthly retirement benefits:

• Normal retirement at age 66; full benefit of $1500 per month starting at age 66.

• Early retirement at age 62; benefit reduced by 25% starting at age 62.

• Extended retirement at age 70; benefit increased by 30% starting at age 70.

Charles never thought much about social security; he usually thought of it as amonthly deduction from his paycheck that helped pay for his parents' retirementbenefits from social security. But this time he decided an analysis should be performed.Charles decided to neglect the effect of the following over time: income taxes, cost-of-living increases, and inflation. Also, he assumed the retirementbenefits are all received at the end of each year; that is, no compounding effectoccurs during the year. Using an expected rate of return on investments of 8% peryear and an anticipated death just after his 85th birthday, calculate the following for Charles:

1. Calculate the total future worth of each benefit scenario through the age of 85.

2. Plot the annual accumulated future worth for each benefit scenario through the age of 85.

The report also mentioned that if Charles dies this year, his spouse is eligible atfull retirement age for a benefit of $1600 per month for the remainder of her life.If Charles and his wife are both 40 years old today, determine the followingabout his wife's survivor benefits, if she starts at age 66 and lives through her85th birthday:

3. Present worth now.

4. Future worth for his wife after her 85th birthday.