A portfolio consists of $3$bonds$,$ A$,$B$,$and C$.$You are given that:

A is a zero$-$coupon bond. It has $10-$year maturity, $5\%$YTM$,$and $$1,500$par value.

B has $3\%$coupon payments made annually. It has $3-$year maturity, $4\%$YTM$,$and $2,000$par value.

C pays its coupon annually and has $6\%$YTM$.$It is currently trading at $$750.$

Part $1)$If the macaulay of the portfolio is $6$years$,$ determine the modified duration of C$.$

Part B$)$Calculate the modified duration of the portfolio

PartC$)$Calculate the above percentage change in the price of the portfolio estimated using the modified duration from above when yield goes down by $25$basis points for all bonds. Note: If you expect an increase or decrease.