A $5-$year $$1,000$ face value bond pays annual coupons. Its current market price is $$950.$ The annual coupon rate is $4\%.$

Find out the bond's yield to maturity.

Find out Macaulay's duration and the modified duration of the bond.

If the bond yield decreases by $25$ basis points $(0\mathrm{.}25\%$ or $0\mathrm{.}0025),$ find out the changed bond price $($no convexity to be considered here$).$

Find out the percentage change in the bond price considering the convexity of the bond $=100.$