Modified Duration in Semi-Annual periods converted to Annual

Why is it that to convert a Semi-Annual Modified Duration to an Annual one, we divide by 2 instead of multiplying by 2? Surely it doesn’t imply that the bond price will move more in half a year than in one full year when interest rates shift?

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Solved: Example 2 A loan of 6 semi-annual payments of #4,500 are to be made to pay for a loan at 5 [algebra]