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 start on the day of your retirement, and which will pay as follows:

(a) At the end of every whole year after your retirement, starting with the first year and ending on the 10th year after your retirement, you will get $20,000.

(b) In the middle of each year after your retirement, for all 10 years that this annuity will run, you also get $10,000. In other words, $10,000 payments would be made at 6, 18, 30, 48, ... months after your retirement, the last payment being made exactly 6 months before the 10th anniversary of your retirement.

What is a fair price today for this annuity?