A long-term zero coupon bond with 3-year maturity, and bond’s market yield was 8% p.a.compounded semi-annually with $100 face value, the price of the zero coupon bond isand the duration of this bond is .A. $79.38, 3 yearsB. $79.38, 2 yearsC. $79.03, 3 yearsD. $88.90, 1 yearE. None of these are correct

Let's break this down step by step:

1. We're talking about a zero-coupon bond. This is a type of bond where you don't get any interest payments. Instead, you buy the bond for less than its face value, and when it matures, you get the full face value. It's like buying a toy on sale for $10, keeping it unopened, and then selling it for the full price of$20 a few years later.

2. The bond has a face value of $100. This is the amount you'll get when the bond matures. It's like the$20 you'll get from selling the toy.

3. The bond matures in 3 years. This is how long you have to wait before you can sell the bond (or toy) and get the face value.

4. The bond's market yield is 8% per year, compounded semi-annually. This is like saying if you put your money in a bank instead of buying the bond, the bank would give you an 8% return on your money every year, calculated twice a year.

Now, we need to find the price of the bond. This is the amount you need to pay to buy the bond. It's like the $10 you paid for the toy.

To calculate the price of the bond, we use the formula for the present value of a zero-coupon bond, which is:

Price = Face Value / (1 + Yield/2)^(2*Years)

So, if we plug in the numbers:

Price = $100 / (1 + 0.08/2)^(2*3) =$79.38

So, the price of the bond is $79.38.

The duration of the bond is the time you have to wait before you can sell the bond and get the face value. In this case, it's 3 years.

So, the correct answer is A. $79.38, 3 years.