Jenna Hawthorne was given a car upon graduation from college. Jenna, however, has been trying to decide how much of her new salary to save for retirement. Jenna believes she could easily save $3,000 of her $45,000 salary. She is considering putting her savings in an annuity fund. She just turned 22 and has a long way to go until retirement at age 65. The fund she is looking at has earned an average of 9% over the past 15 years and can be reasonably expected to continue earning this amount, on average. While she has no current savings, five years ago Jennas grandparents promised her an account valued at $10,000 after 30 years. Jenna wants to know her retirement income if she both (1) asks her grandparents for an early inheritance and invests the proceeds in the stock fund and (2) saves an $250 at the end of each month in annuity fund from now until she turns 65. Once she retires, Jenna wants those savings to last for 25 years until she is 90.

1. Suppose the account Jennas grandparents set up has an interest rate of 6.5% APR compounded semi-annually. If she liquidates the account today, how much would be in the account?

2. Suppose Jenna liquidates the account and reinvests the funds in the annuity fund and saves as planned. If, indeed, Jenna ears a 9% annual return on her savings, show much could she withdraw each year retirement? Assume she begins withdrawing the money from the account in equal amounts at the end of each year once her retirement begins.

3. Jenna expects her salary to grow regularly. While there are no guarantees, she believes an increase of 4% per year is reasonable. She plans to save $250 at the end of each month and then increase the amount she saves by 4% each year as her salary grows. Unfortunately, prices will also grow due to inflation. Suppose Jenna assumes there will be 3% inflation every year. In retirement, she will need to increase her withdrawals each year. In this case, how much can she withdraw at the end of the first year of her retirement? What amount does this correspond to in todays dollars?

4. Should Jenna liquidate her inheritance account and invest the proceeds in the annuity fund? Give one reason in favor of this plan and one reason against this plan.

5. Suppose Jenna has overestimated her ability to save and the economic conditions going forward. Instead of saving $250 at the end of every month, she is able to save $175 each month. Additionally, the annuity account earns only 7% each year and her salary increases by only 1% each year. How does this change Jennas retirement plan?