Elizabeth has worked for State Government for 27 years. She is currently making $90,000 and plans to retire at the end of three years (with 30 years of service). She qualifies for the PERS1 plan, which will pay a retirement benefit of 2% for every year of service, up to a maximum of 60% of the average of her final two years pay.

Elizabeth expects to receive a 3% raise each year for the next (and last) three years of her employment.

Many years ago, Elizabeth began contributing to an IRA. Someone once advised her to put the money away and ignore it so Elizabeth hasnt even looked at the annual statements for her IRA account. She leaves them sealed and puts them in a shoebox in the garage. Now that shes close to retirement she guesses she should see if she really will be able to afford to retire.

Elizabeth wants to have $75,000 retirement income in real terms (meaning current dollars). She has always assumed that she would earn 5% annually on her investments after subtracting for inflation. Although she does not know if that is correct, she is going to continue to use that assumption. Shes careful about her health, gets lots of exercises, and eats wisely so she figures shell live for another 30 years.

1. Calculate Elizabeths income for the three years -- 28 through 30. Show your work.

2. What is the average of the last two years of her employment?

3. Calculate the value of Elizabeths annual retirement income from the State. 4. Elizabeth does not know what will happen with Social Security in the future. She is assuming that all of the shortfalls will have to come from that mysterious IRA. Given that assumption, what is the annual shortfall that Elizabeth will have?

5. How much will have to be in the mystery account on the day that Elizabeth plans to retire in order to meet her income goal? State any assumptions that you make.