A writer plans to write a new book over the next two years. She will get an advance of $$200,000$ immediately. However, the opportunity costs of writing the book instead of working for a newspaper are $-$$$400,000$ immediately $($at time $0),$ and another $-$$$200,000$ in the two years she will write the book $($times $1$ and $2).$ The book will be released at the beginning of year $3,$ and the writer's contract stipulates that she will collect royalties of $$100,000$ per year for $10$ years after that $($times $3$ though $12).$ What is the net present value $($NPV$)$ of this decision to the writer if her opportunity cost of capital is $10\%?$

Group of answer choices

$-$$$166,245\mathrm{.}84$

$$87,661\mathrm{.}89$

$-$$$39,291\mathrm{.}97$

$$11,489\mathrm{.}57$