I assume that by volatility you mean duration. Otherwise, please clarify.

The problem states that both portfolios have the same volatility (or, duration). Therefore, each portfolio will be on each side of the equation.

Duration of Portfolio B equals four years because it only consists of a four-year, zero-coupon bond. Check the formula in the aforementioned link to see why: t=4 is factored from the numerator; that leaves the rest of the numerator equal to the denominator, and thus they "cancel".

Applying the Duration formula to Porftolio A leads to the equation:

(70*v+2*70*v

^{2}+3*70*v

^{3}+4*1070*v

^{4}+5*X*v

^{5}) / (70*v+70*v

^{2}+70*v

^{3}+1070*v

^{4}+X*v

^{5})= 4

Solving the equation for X gives the answer.

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