What is the duration of a $$1000$ Treasury bond that pays $10\%$ annual coupon and has $2$ years remaining to maturity? The current yield is $8\%.$ If the current yield increases to $10\%,$ what happens to the duration?

Multiple Choice

$19106$; increasing the yield to maturity decreases the duration of the bond

$1619,$ increasing the yield to maturity decreases the duration of the bond

$19106$; increasing the yield to maturity increases the duration of the bond