A $10\%$ coupon $$1,000$ par value bond with four years to maturity is currently selling for $$900.$ The bond pays coupon payments on a semiannual basis. If interest rates move in the corporation's favor, the bond will be called for $$1,050.$

What is the effective duration of the bond?

$3\mathrm{.}50$ years

$9\mathrm{.}50$ years

$15\mathrm{.}25$ years

$19\mathrm{.}75$ years