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 .
Question
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 .
Solution
Alright, let's break this down.
A zero-coupon bond is like a gift card. You buy it for less than what it's worth, and after some time, you can use it to get something that's worth more. In this case, you're buying a bond that's worth 100 for it.
The bond has a 3-year maturity, which means you have to wait 3 years before you can use it. It's like having a gift card that you can't use until 3 years later.
The bond's market yield is 8% per annum compounded semi-annually. This is like saying, if you had $100 and you put it in a bank, the bank would give you 8% interest every year, and they would calculate this interest twice a year. So, after six months, you'd get 4% of your money as interest, and then six months later, you'd get another 4% of your money plus the interest you got before.
The price of the zero-coupon bond is the amount you need to pay to buy the bond. It's like the price you pay for the gift card.
The duration of the bond is the time you have to wait before you can use the bond. In this case, it's 3 years. It's like the time you have to wait before you can use your gift card.
So, to sum it up, you're buying a 100 (the price of the bond). You have to wait 3 years (the duration of the bond) before you can use it. And if you had put that $100 in a bank instead, the bank would give you 8% interest every year (the bond's market yield), calculated twice a year.
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