Consider a $5-$year bond with a par value of $$1,000$ and an $8\%$ annual coupon. If interest rates change from $8\%$ to $7\%$ the bond's price will:

a$.$

decrease by $$53\mathrm{.}46.$

b$.$

decrease by $$41\mathrm{.}00.$

c$.$

increase by $$41\mathrm{.}00.$

d$.$

increase by $$53\mathrm{.}46.$