When you retire at $65$ you can take either $$500,000$ in cash, or an ordinary annuity that pays $$47,488\mathrm{.}98$ per year for as long as you live. What is the present value of the annuity if you only live $24$ years an

if the current rate of interest is $8\%?$

$$510,000$

$$520,000$

$$550,000$

$$500,000.$