A $65$ year$-$old male retiree has a $$600,000$ SGS lump sum with which to provide for his retirement income. He owns his own home and has $$50,000$ in lifestyle assets.

He decides to spend $$550,000$ on a guaranteed $30-$year annuity, indexed at $3\%$ p$.$a$.$ and payable monthly in arrears. It has zero residual value. The remaining $$50,000$ is invested in an S&P$200$ ASX Accumulation Index Fund over the guaranteed income years to provide emergency capital or residual capital in the event the retiree outlives the $30-$year annuity.

a$)$ Find the annuity unit cost if it can be purchased at a yield of $4\mathrm{.}25\%$ p$.$a$.$ effective and hence state the dollar amount of the retiree's starting annual annuity.

b$)$ What fortnightly amount of Age Pension would he be entitled to claim?

c$)$ What alternative strategy would you recommend in relation to generating a Retirement Income Stream from the lump sum accumulation? Explain.