In this workout. We are asked to calculate the modified duration for the following Bond. The bond which has a settlement date of the 1st of January 2030 and maturity date of the 1st of January 2034. So we've got four years to maturity. I've got a coupon rate of 3.5% a yield to maturity of 5% and a frequency of one which means we have an annual coupon payment is made once per year.

We also have a par value here of 1,000. So to calculate modify duration we're going to first of all need a Macaulay duration number because the modified duration is modifying the Macaulay duration number. So we're going to use our Excel function for duration. Here to calculate McCall iteration. So we need the settlement date. We need the maturity date. We need the coupon rates the yields maturity and then the frequency.

So this will give us a Macaulay duration of 3.80. Which is less than the time to maturity of four years because some of the cash flows are received before that maturity date To calculate modified duration. We need to take them accordion and modify it by dividing it by 1 plus the yield to maturity.

Divided by the number of payments per year or in other words the frequency. Now because the frequency here is just one that has no impact on this calculation, but that's how we need to do this correctly. To give us a modified duration figure of 3.61. Well, this modified duration figure is telling us is that if there is a 1% change in yields then approximately there'll be a 3.61% change in the price of the bond in the opposite direction.

We can also get modified duration using an Excel function. That function is the m duration function.

And for the M duration function, we have the same inputs as we do for the duration function, which is that we need a settlement date a maturity date a coupon rate. a huge maturity and a frequency and that will give us the modified duration of 3.61 the same number that we arrived at with our formula calculation.