Your parents will be retiring in three years and want to have $1,000,000 in pension assets. At the beginning of 2009, they have accumulated $700,000. Because of their long history with the company, it has agreed to contribute $36,500 equally at the end of 2009, 2010, and 2011. The company’s rationale was that, at an interest rate of 8%, your parents would have slightly more than the desired $1,000,000 when they retire on January 1, 2012.
Required:
(a) Prove that the company’s calculations are correct.
(b) Assume that the retirement account for the next three years did not perform at the level company management had predicted. Actual returns for each of the years were as follows: 2009, 2%; 2010, 3%; and 2011, 5%. How much will your parents have when they retire on January 1, 2012?