Randy currently has an obligation that he will pay $1 million a year for the next 3 years, what is the duration of his obligation if the appropriate discount rate is 5%?

If Randy wants to immunize his obligation using a 1-year zero coupon bond and a perpetuity both yielding 6%. I rounded the durations to two decimal places to minimize rounding errors.

What is the weight he should invest in the zero?

What is the weight he should invest in the perpetuity?