QUESTION 2 (30 MARKS)

CTDK Corporation wishes to accumulate funds to provide a retirement annuity for its Vice President, Mr. Xing Zhao Lin. He will retire at the end of exactly 12 years. On retirement, he is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If he dies prior to the end of the 20-year period, the annual payments will pass to his heir, Ms. Liang Jie.

During the 12-year accumulation period, CTDK Corporation wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 4.45 percent interest. Once the 20-year distribution period begins, CTDK Corporation plans to move the accumulated monies into an account earning a guaranteed 11.50 percent per year. At the end of the distribution period the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.

1. How large must CTDK Corporations equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Mr. Xings retirement annuity?

1. How much would CTDK Corporation have to deposit annually during the accumulation period if it could earn 6 percent rather than 4.45 percent during the accumulation period?

2. How much would CTDK Corporation have to deposit annually during the accumulation period if Mr. Xings retirement annuity were a perpetuity and all other terms were the same as initially described?