Assume that you are a financial analyst in the fixed income department of an investment bank. You are given the following information: the 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are, respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, with continuous compounding. Your task is to answer the following questions.

1. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4% per annum semiannually.
2. Calculate the yield rate of this bond.

Please show all calculations and explain in detail each step you took to get the answers.