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, $2\%$ 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 $5\%$

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 $30$ basis points for all bonds. Note: If you expect increase or decrease.