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Question $18$

$10p$

Congratulations $-$ You have just won a lottery!

The lottery gives you two options:

Option A:

You will receive $10$ equal annual payments of $$50,000$ each at the end of years $1$ through $10,$ followed by equal annual payments of $$x_{?}$ from year $11,$ forever.

Option B: Lumpsum $($one$-$time$)$ payment of $$1,000,000$ today.

If you are indifferent between options A and $B,$ find the value of $x.$

Assume that the interest rate is $12\mathrm{.}00\%$ per year, compounded monthly.

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