In this workout, we're asked to calculate the duration or more correctly the Macaulay duration for the following Bond. With others Bond was issued or purchased on the 1st of January and it's maturity date was on the 1st of January five years later. So we have a times maturity of five years. We've got a 2% coupon rate that is an annual coupon and we've got a 5% yields maturity. So in terms of calculating our duration, what we first of all need to do is to model the cash flows on the bond, which we can get by taking the coupon rate and multiplying it by our value which here we're going to take as a hundred every Year's cash flow is going to be the same after that as well so we can copy that down. And then in the last year, we will also receive the par value which here we're going to assume is a hundred as well. So we'll get that back in the fifth year giving us 102 as our cash flow in the fifth year. We then need to present value each of these cash flows and we're going to do that by calculating our discount factor, which is what we need to multiply the future Cash Flow by to turn it into its present value. So our discount Factor one divided by 1 plus our discount rate or our yield and we're going to lock on to that. To the power of the number of the year that we're in. So for the first Year's cash flow when we need one years worth of discounting. we can then copy that down for each of the five years and then We can calculate the present value of each Year's cash flows by multiplying that yes cash flows by the discount Factor. This will give us the present value of each Year's cash flows. Which if we add that all up it will give us the price of the bond. To calculate our duration number or Macaulay duration. We then need to multiply together the present value of the cash flow for each year with the number of the year that we are in. So our first year is cash flows need to be multiplied by one. The second Year's cash flow needs to be multiplied by 2. and if we do again that for all of the five years We will then get to the present value multiplied by the time period when that cash flow is received for each year. We then need to add up all of those numbers. So we're going to get the 416.9 here in that final column. To calculate the Macaulay duration. We need to take the sum of each Year's cash flow multiplied by the year when the cash flow is received and divide that by the sum of their cash flows. or in other words the price of the bond They should therefore give us a Macaulay duration for this Bond. Of 4.8. For which the units are in years. So what we're effectively saying here is that we have to wait 4.8 years to receive the cash flows on this one weighted by the present value of those cash flows. For any coupon paying Bond the duration will be less than the time to maturity because some of the cash flow is received before that maturity date here in five years time and alternative way of calculating your Macaulay duration is to use the duration function within Excel for this function. We need to first of all tell XL what the settlement date is. Which is the 1st of January of 2000s. We then also need to tell Excel the maturity date first, January. 2005. Next is the coupon rates 2% Then the yield in percentage terms 5% And then the last time we need to tell Excel is the frequency of our cash flows, which here is just going to be annual. So the number one here represents cash flows happening once per year. This will also give us the Macaulay duration. of this bond to be that 4.8 years 4.79 if we want to go to two decimal places.