00:01
To calculate the bond's approximate modified duration, we can use the formula for modified duration, which is d over 1 plus y, where d is the lower quality duration, which is the weighted average time until cash flows are received, and why is the yield to maturity as a decimal? so for the bond, we have a $100 par value, a 5 % coupon rate.
00:21
So the coupon payment is going to be 5 % of 100, which is 5, and y is going to be 0 .03.
00:28
The cash flows for year 1 or 5 to year 2 or 5 and 3 would be 5 plus 100 or 105.
00:37
We need to calculate the present value of each cash flow using the yield to maturity of 3%.
00:43
So the present value for year 1 would be the cash flow for year 1 over 1 plus .03 to the 1st, which would be 5 over 1 .03, and that's 1 .3.
01:04
About 4 .844.
01:07
For year two, that would be 5 over 1 plus 0 .03 to the second, which is about 4 .716...