For the following transaction of a 2022 June, 6% coupon rate Commonwealth Government Security (CGS), with a 6% coupon. Assume the par value is 100, and YTM is 5% P.A. Please keep 4 decimal places.

1. If transaction date is 9 th of June, calculate the price of the bond using dirty price (Notice: 2020 is a leap year).

2. Assume you bought this CGS on 15th of June 2018 (immediately after the previous coupon payment) for $115, and the CGS was sold to Jack for $110 on 15th of June 2020 (after you receive coupon payment). Coupons can be reinvested at the YTM rate, how much is your total return per year?

3. Assume after the 15th of June 2021, in the market, a similar one-year CGS yield decreases by 2%, calculate the modified duration for such CGS.