Newton owns a $5\%$ bond that has $5$ years to maturity and an $16\mathrm{.}8\%$ yield to maturity $($YTM$).$ If the YTM on the bond decreases to $10\mathrm{.}2\%,$ how much will the bond change in value?

$$Increase by $$169\mathrm{.}21$

$$Increase by $$189\mathrm{.}06$

$$Decrease by $$189\mathrm{.}06$

$$Decrease by $$169\mathrm{.}21$