Determining the duration of a single cashflow or zero coupon bond is straightforward. But what about coupon paying bonds? In this example, the first four columns are dedicated to getting the price of a bond. If we add up the fourth column, it leads to 102.78. This represents the price of this bond at its required yield of 4%. The percentage PV is the proportion of the value that each cashflow represents in the price. For example, the 4.68% in the first row represents the proportion of the 4.81 PV in the total price of 102.78. If we multiply the percentage PV by the number of the year when it's received, this will give a weighted average of the time until each cashflow is received. Overall, this leads to the number 2.8614.

This says that an investor will have to wait 2.86 years on average to receive the cash flows from this bond. Bonds with a higher Macaulay duration will have more interest rate risk. The modified duration takes the Macaulay duration and modifies it. It gives a number that doesn't only give a measure of relative risk as Macaulay duration does, but tries to express the amount of risk faced in terms of how much a price of a bond might change as interest rates change. To calculate the modified duration, first calculate the Macaulay duration, then modify the calculation by dividing it by one plus yield. Modified duration can be interpreted as the approximate change in the price of a bond if interest rates were to change by 1%. This example, the modified duration of 2.7514 means that if interest rates were to change by 1%, the price of the bond would move by around 2.75% in the opposite direction.