The six month and one-year rates are 3% and 4% per annum with semi-annual compounding. Is 3.90% or 3.95% or 3.99% closest to the one-year par yield expressed

this question is asking one-year value @ par bond yield. Because value @ par, Yield = Coupon rate. 

Assume face value 100 (can be eliminated later)

Denote Yield to be Y, build up equation to calcuate Bond Yield. 

Left Hand Side you have DCF of Coupon and Principle using 3% and 4%

Righ Hand side you have DCF using Y, 

they are equal. You get a third order equation wil the only unknown variable Y.

you will arrive at answer Y=3.99%

Your question is not very clear!. The 6-month rate of 3% is only for 6 months. So if you copounded it, you will get 1.03^2=6.09% equivalent annual rate. 4% compounded semi-annualy is eqivalent to 1.02^2=4.04% effective annual rate. So, you can compare the numbers you gave to these rates that I calculated.

Im actually don't understand what is the question asking about. can you help me please

Well sir. You posed the question. Who gave it to you? Ask them to clarify what they mean. I think they are trying  to compare interest rates when compounded to nominal rates. But I'm just guessing as to their intent.

What i got is 3.90 = 3.86%

3.95 = 3.911% 

3.99 = 3.95%

Is 3.99 the answer for this question? that's what it was asking about right.

OK sir. Now I understand what they are doing: they have given a bunch of nominal rates and they are converting them to annual effective rates, and they are compounding them semi-annualy:

So, what does that mean? It means as follows:

1-3.86% componded semi-annually is the same as 3.90% compounded annualy.

2-3.911% .................................................................3.95%...................................

3-3.95%....................................................................3.99%...................................

That's ALL it means. They are simply converting interest rates from compounded semi-annually to compounded annually. So, All the figures on the left hand side are equivalent to the right hand side when componded semi-annually. In other words, 3.95% compounded semi-annually is exactly the same as 3.99% componded annually.

To the asker don’t pay too much attention to this anon answer man. He is pompous and fussy and think he know everything  like he call you sir but I know you are a Miss. I call him Retentive because he is Anol. hahaha

Any way Retentive not answer the question right because he not understand it.