Answer the following questions considering a bond portfolio comprising four bonds, each with face value of $1000, as follows:

A treasury zero-coupon bond maturing in 8 years and currently yielding 7%

BB-rated corporate bond maturing in 10 years, offering 9% coupon paid semiannually, and currently yielding 11%.

AA-rated corporate bond with a 9% coupon paid semiannually currently yielding 8% with 7.5 years to maturity.

AAA-rated corporate bond with a 7.5% coupon paid semiannually maturing in 10 years and trading at par.

Calculate the duration of the portfolio in years

Calculate the portfolio modified duration in years

What is the percentage change in the value of the bond portfolio with a decrease in interest rates of 50 basis points