You are planning to establish a retirement savings plan by setting aside money at the end of each year. It is your hope to retire at age 55 with a pension income of $100,000 per year received at the end of each year, for 20 years, from the money accumulated in this fund. You expect to earn 8% per year on the fund assets as they accumulate, and on retirement, you expect to purchase a 20 year annuity earning 6% on the undrawn balance. You are now 30 years of age. Ignore inflation.

a. How much money will be required in the retirement fund to purchase the annuity when you are 55?

b. Starting now, you plan to make annual (at year end) contributions to the retirement fund of $13,000. Will that be sufficient to meet your goal? If not,

i. What rate of return would you need on the fund to reach your goal with these contributions?

ii. Assuming the 8% return, how much would you have to contribute annually to reach your goal?