Assume that interest rates are at $7\%$ per annum, compounded semiannually. You will retire exactly $20$ years from today. Your financial adviser suggested that you buy an annuity that will pay as follows:

At the end of every whole year after the day of your retirement, and ending at the end of the $10$th year after your retirement, you will get $$20,000.$

In$-$between each $20,000$ payment, you also get $$10,000.$ These payments will be made exactly $18,30,42...$ months after the day of your retirement, the last payment of this type being made exactly $6$ months before the $10$th anniversary of your retirement.

What is a fair price today for this annuity?