A zero coupon bond has a par value of $$1,000$ and matures in $6\mathrm{.}5$ years. The yield to maturity is $5\mathrm{.}5\%.$ What is the Macaulay duration?

$5\mathrm{.}67$ years

$5\mathrm{.}81$ years

$5\mathrm{.}92$ years

$6\mathrm{.}26$ years

$6\mathrm{.}50$ years