Janet lopez wishes to establish a trust fund from which her son can withdraw $15000$ every $6$ months for $21$ years $,$ when he reaches $25$ years old. at the end of which time he will received the remaining money in the trust, which she would like to be $100,000.$ the trust fund will be invested at $7\%$ per annum compounded semi$-$annually. how large should the trust be$?$