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 pair of successive $$20,000$ payments, you also get $$10,000.$ These

payments will be made exactly $18,30,42,$dots 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?

Hints$/$Notes:

A$.$ This question is harder than the rest.

B$.$ Could you decompose the annuity above into two or more annuities that together form the

original annuity? If so$,$ then valuing the component annuities will help you determine the

value of the composite annuity.

C$.$ Remember that when valuing an annuity, you must use the interest rate that corresponds to

the time period $($interval$)$ between the payments of the respective annuity.

D$.$ We recommend that you use $4-5$ decimals when computing intermediate results. Round your

final answer to $2$ decimals.

E$.$ Provide the answer as a positive number!