We have an annual rate. It is compounded monthly. All the payments are semi-annual. It is a mass of confusion.
i = 0.16
There, now we have a semi-annual discount factor.
Step 2) BEFORE all else fails, consider basic principles. Practice this. Get good at it.
From here on out, I will just use 'v'. Understand this to mean the semi-annual discount factor.
Just write it down.
There. It is done. That is the present value you seek.
Of course if you would like to simplfy it, feel free.
You should recognize the right-most piece.
How are we doing?
$10,000*0.48907362*7.17698305 = $35,100.73
Note: I used machine rounding. I would guess this is 15 decimal places. If I use the numbers I actually typed here, rounding each intermediate result to 8 decimal places, I get:
$10,000*0.48907376*7.17698392 = $35,100.75
This demonstrates rather clearly that your "answer" is using a different rounding convention. In any case, you should see the idea. When you implement your rounding conventions, you should be in the neighborhood.