 There is always a risk of changes in interest rates in any economy. Now the concept of duration is a principal determinant of interest rate changes riskiness. Now let's see the impact of changes in interest rates on the bonds prices. We have a world where the market interest rate is 10% and there we have a zero coupon bond with the face value of $100. Now for this type of bond, the present value of bond having one year maturity is equal to $100 and the present value of such bond with five year maturity is also equal to $100. Now let's see what will be the changes on the bond prices if there is any change in the coupon rate of interest. We have a table that is showing the interest rate movements and this next column is a one year period of the discount bond and second is the five year period of the pure discount bond. So we are valuing two bonds of two different majorities using three different interest rates. Rates are 8% 10% and 12%. If we look at the table, we can conclude that the long term pure discount bonds are more volatile than the short term pure discount bonds and that is evident while we see at the price movements of the five years maturity bond. Next we have another case where the case is of two bonds with the same maturity but we have different components. On the left side we have three panels. The upper panel is about a 10% coupon bond having five year maturity and the middle panel is on a 1% coupon bond having five year maturity and the last panel is the comparison of 10% coupon bond and 1% coupon bond with the interest rate changes from 10 to 8% and 10 to 12%. If we sum up the changes in these panels, we can see that for interest rate 8%, 10% and 12%, the 10% bond is more volatile than the 1% coupon bond. As we can see that the price movement in these two types of bond is much higher for 10% bond. Then we see that for each of the 10% and 1% coupon bonds, worth is more for 8% than 10% and that we can see in our lower column. So we see that the price changes on 1% bonds are greater than the percentage changes on the 10% bond. We know that price volatility of a pure discount bond is generally determined by its maturity and by duration we mean an average of maturity of the bond's cash flows weighted by the present value of each periodic individual cash flow of the bonds. Now how to compute this average maturity of the bond? It happens in three steps. At first step, we need to calculate present value of each coupon of the bond and that is the periodic interest payment and the last cash flow on the face value of the bond. Then we need to develop a relationship between the individual periodic coupon cash flow over the total present value of the bond. And at third step, we need to compute each cash flows weighted maturity. Now to understand this three step model, we have an example where we have a coupon bond, 10% coupon bond with the face value of $100 having maturity period of five years. Now we can determine the bond's maturity using this particular data. We are doing this in three steps at first step in the first upper panel of the screen. We see that we have calculated present value of individual coupon on the bond. Then we have expressed the present value of individual coupon with the total present value of the bond. And in the final stage, we are multiplying individual years number with its corresponding present value. In this way, we have determined the total maturity of the bond as the duration of this particular bond. And this duration is 4.169 years or 4.17 years. So using this model, we can also determine the duration of a one year one person to coupon bond. And for one person coupon bond, the duration is 4.8740 years. So we have two duration periods for two different coupon bond having same maturity. We see that the percentage price changes of a higher duration bond are greater than percentage price changes of a lower duration bond. We can translate this into another way that one person bond have greater duration than 10% bond even both have a similar amount of maturity period. And that is five years in our case. The one person, the reason of this variation is that the one person bond receives only $1 in each of the first four years as the individual years coupon amount of interest. So it has lower weighted in the weighted basket. For the 10% bond, the holder of the bond receives $10 cash flow in each of the four years as the individual periods interest payment. So the amount is big. Therefore, its weighted value is big. And as a result due to higher weighted value, the duration of this bond will be lesser than the duration of the lower coupon bond.