The semi annual bond is worth more when trading at a premium and the difference lies in the reinvestment risk as noted by Harrogath. When the market rate exceeds the bond rate there is reinvestment risk.

### 2) Key Bond Characteristics

When the bond rate exceeds the market rate there is no reinvestment risk. Both bonds sell at a discount however with the semi-annual coupons, I can reinvest for an extra 6-months at a higher market rate hence it has a higher present value than the annual bond. The premium is smaller as the coupon rate is closer to the market rate.

The difference between the annual and semi-annual is larger as you are compounding for an additional 6 months at a higher rate. I understand why the bonds trade at a discount or premium based but I do not understand the reinvestment risk aspect. If I received a discount halfway through the year, could I not invest that coupon at the market rate guaranteed and hence earn more through additional compounding? What you mean is that you should have converted the annual, nominal rate to a semiannual nominal rate, and you should just say so.

This really surprises me, because I know you to be much better than to make this sort of silly mistake. This is all silliness. When there are interim cash flows there is always reinvestment risk, regardless of the market rate. When there are no interim cash flows, there is never reinvestment risk, regardless of the market rate.

### Present Value of Payments

That explained it perfectly. I want to apologize for such a foolish post I made. Indeed I was wrong on my response fueled by a big confusion of mine. Skip to main content. Be prepared with Kaplan Schweser. Twitter Facebook LinkedIn. Search form. PompeyCrassus Apr 7th, am. Studying With. Is this right? Harrogath Apr 7th, am. GrahamDoddFisher Apr 7th, am. PompeyCrassus Apr 7th, pm. If I use the effective semi-annual rate for discounting I get the following.

The interest rate remains fixed throughout the life of the zero coupon bond, so the price to buy the bond has to change throughout its life to match equivalent yields already out there in the market. Zero coupon bonds typically have long maturity periods and can take 10 or more years to pay out. Because of this, prices fluctuate wildly on the secondary market. Because of the discount on the original purchase and opportunities to buy on the secondary market, these bonds can be a good way to provide a lump sum return at a specific time for a long-term goal, like paying for a child's college.

The basic method for calculating a zero coupon bond's price is a simplification of the present value PV formula. Zero coupon bond prices are typically calculated using semi-annual periods twice a year because bonds that offer a coupon often pay interest twice a year. So, calculating the price of a zero coupon bond this way allows Tom to compare investing in this zero coupon bond to investing in a traditional bond.

So, because the required interest yield is a yearly figure, it has to be divided by two to make the yield semi-annual. In addition, the number of years until maturity has to be multiplied by two since, again, coupon bonds pay out twice a year. Now that he knows the formula and understands its components, let's see how it all works.

To determine n for our formula, we take the number of years to maturity and multiply by two. What does this mean in plain English for Tom?

If he pays more than this, his yield will decrease. But, he stands to make an even greater return if he can beat that price.

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A zero coupon bond is a bond that doesn't make any periodic interest, or coupon, payments and instead pays only the full face value on its maturity date. For investors to realize a return, the bond must be bought at a price below face value. M is the face value at maturity, i is the desired yield divided by 2, and n is the number of years remaining until maturity times 2.

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- Definition.

This formula can show the maximum price to pay to achieve a desired yield or calculate the yield an investor will earn based on a specific purchase price. To unlock this lesson you must be a Study. Create your account. Already a member? Log In. Already registered?

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## Bond Price

Quiz Course. Try it risk-free for 30 days. Add to Add to Add to. Want to watch this again later? Zero coupon bonds are an alternative investment type compared to traditional bonds.

## Example 10 coupon bond with semi annual coupons face value of 20 years to

In this lesson, we will explore what makes these investments unique and how investors can calculate a purchase price or yield of these bonds. Zero Coupon Bonds Most bonds make periodic interest payments to pay back bondholders for borrowing money. Definition A zero coupon bond is a type of bond that doesn't make a periodic interest payment.

Pricing Maturity dates and interest rates dictate the price of zero coupon bonds. Formula and Example The basic method for calculating a zero coupon bond's price is a simplification of the present value PV formula. Try it risk-free No obligation, cancel anytime. Want to learn more? Lesson Summary A zero coupon bond is a bond that doesn't make any periodic interest, or coupon, payments and instead pays only the full face value on its maturity date.

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