You have been offered a unique investment opportunity. If you invest $ $9$ comma $100$today$,$ you will receive $ $455$ one year from$$ now, $ $1,365$ two years from$$ now, and $ $9,100$ ten years from now.

a$.$ What is the NPV of the opportunity if the cost of capital is $6\mathrm{.}2\%$ per$$ year? Should you take the$$ opportunity?

b$.$ What is the NPV of the opportunity if the cost of capital is $2\mathrm{.}2\%$ per$$ year? Should you take it$$ now?