Zero Coupon Bond Calculator

When the term zero-coupon bond comes, the two words urgently come into mind; one is the pure discount bond, and the other one is the discount bond. Both of these words represent the common zero coupon bond term. Zero Coupon bond is also named as accrual bond and it lacks the coupons or the installments procedure for making the payments; instead, a single payment at the level of maturity (the time period or the duration) is paid. The amount that one pays at maturity level is called face value or par value. Here the term discount bond refers to the discounted selling criteria of something that vary according to the face value instead of fixed pricing standards as we see other than this way.

How is Zero Coupon Bond Yield Calculated?

There is another concept that is required to understand while doing all these calculations is the concept of yield. What actually the zero coupon bond yield is? So, to answer this question, it is necessary to mention that the yield is basically the periodic return of a zero-coupon bond. Now the thing to understand is how this yield is calculated, so for that, and there is a particular formula in terms of economics that helps us to calculate that yield. The formula is mentioned below:

• Zero-Coupon Bond Yield =       F     1/n
•     PV       – 1
• Here;
• F represents the Face or Par Value
• PV represents the Present Value
• n represents the number of periods

I feel it necessary to mention an example here that will make it easy to understand how to calculate the yield of a zero-coupon bond. For instance, if a person buys such a bond at $1000, whose face value at the time of maturity is $2000. It is an obvious thing that no coupon is paid periodically; that person will get the return back at that maturity or upon selling it, seeming that the rates will remain totally constant.

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What can a Semi-annual price calculator do for you?

When we aim to get a zero coupon bond price calculator semi-annual, the easy way is to have the coupon rate on the bond and then divide it by the present price of the bond to obtain yield. As coupon rates are fixed in terms of yearly interest payments, that’s why it is necessary to divide the rate by two, to have the semi-annual payment.

Suppose you have a bond and its face value is $1000 with the present price of $900, and the coupon rate is 2%. Its maturity period is also five years. So, when we calculate the semi-annual bond payment, first of all, we have to get 2% of the face value of $1,000, which is $20, and after that, we have to divide it by two. The bond, therefore, pays $10 semi-annually. When we divide $10 by the current price of $900, then the semi-annual bond yield will be obtained, which is 1.1%.

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How does Zero Coupon Bond Calculator Works?

The concept to calculate the duration of the Zero Coupon Bond was firstly given by Frederick Robertson Macaulay, who was an economist and belonged to Canada. He portrayed the good maturity concept as the “duration” of the bond. While rendering his services for this, he mentioned that the duration could be calculated as an average of the times to maturity for every bond coupon. The formula to calculate the duration that was given by Macaulay was then remembered as Macaulay’s duration formula, which is written below:

• Macaulay Duration Formula = 1PV∑Tt=1(t×PVt)
• If there is no coupon bond, we can also calculate the duration by using the formula mentioned under:
• Macaulay Duration = 1PV(T×PVT).
• PV = PVT = Face Value (1+r) T
• Therefore:
• Macaulay Duration = 1PV (T×PV) = T

Here:

• D = Macaulay duration of the bond
• T = Periods up to the maturity
• i = the ith time period
• C = payment of the coupon
• r = Periodic yield to the maturity
• F = the face or par value at the time of maturity

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How to Calculate the Price of Zero Coupon Bond?

The particular formula that is used for calculating zero coupon bond price is given below:

• P
• (1+r)t

Examples:

Now come to a zero coupon bond example, if the face value is $2000 and the interest rate is 20%, we will calculate the price of a zero coupon bond that matures in 10 years. Then, the under the given procedure will be applied to get the required answer easily:

• $2000
• (1+.2)10
• $2000
• 6.1917364224
• $323.01

The upper mentioned $323.01 is the actual cost of the 10 years’ maturity coupon with a 20% interest rate and $2000 face rate.

There is another zero-coupon bond example if the face value is $4000 and the interest rate is 30%, and we are going to calculate the price of a zero-coupon bond that matures in 20 years. So, the under the given procedure will be applied to have the demanded answer easily:

• $4000
• (1+.3)20
• $4000
• 190.049637748
• $21.05

The upper mentioned $21.05 is the actual cost of the 20-years maturity coupon with a 30% interest rate and $4000 face rate.