Which one of the following bonds would you select if you thought market interest rates were going to fall by $50$ basis points over the next six$$ months?

a$.$ A bond with a Macaulay duration of $6\mathrm{.}63$ years$$ that's currently being priced to yield $7\mathrm{.}42\%.$

b$.$ A bond with a Macaulay duration of $17\mathrm{.}35$ years$$ that's priced to yield $9\mathrm{.}36\%.$

c$.$ A bond with a Macaulay duration of $8\mathrm{.}53$ years$$ that's priced to yield $6\mathrm{.}83\%.$

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Part $1$

a$.$ The modified duration for a bond with a Macaulay duration of $6\mathrm{.}63$ years$$ that's currently being priced to yield $7\mathrm{.}42\%$ is enter your response here years.$($Round to two decimal$$ places.$)$