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1. Obrien Group wishes to accumulate funds to provide a retirement annuity for its Director of Research, Peter Alexander; Mr. Alexander by contract 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 heirs. During the 12-year 'accumulation period', Obrien wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9 percent interest. Once the 20-year 'distribution period' begins, Obrien plans to move the accumulated monies into an account earning a guaranteed 12 percent per year. At the end of the distribution period the account balance will equal zero. Note 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.

Required:

1. What is the time value of money? Explain using the above scenario and draw a timeline depicting all the Cash flows associated with Obrien's view of the retirement annuity.
2. How large a sum must Obrien accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?

3. How large must Obrien's equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Mr. Alexanders retirement annuity.

4. How much should Obrien have to deposit annually during the accumulation period if it could earn 10 per cent rather than 9 per cent during the accumulation period?

5. How much would Obrien have to deposit annually during the accumulation period if Mr. Alexanders retirement annuity was a perpetuity and all other terms were the same as initially described?

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