Okay, guys, this is Chapter 27 problem. Three. So in this question were given that they're two bombs. Bond A pays $8,000 in 20 years. And Bondi here's $1,000 in 40 years. So the first part of questions asking us that the interest rate is 3% what is the current value of the bonds? So this was a net present value question, and the formula for net present value can be found on Page 5 65 the textbook. The formula is facts, which is the payment you get over one plus the interest rate to the power of and which is the number of years in the future that you're going to receive the payment equal to the Net present value of the first bond. We're going to receive $1,000 on an interest rate of 3% in 20 years, and this is going to equal for $1,020. You can't do this with the rule of 70 like the question that intimate questions says. But it's very easy to do this with formula. I'm so for Bond be it's gonna be 8,000 over one class. The interest rate to the power 40. And this is 2,000 and 20 right? This is bond be. And this is bond, eh? S O. Obviously bond be is worth less. And that's because you have to wait longer to receive the payment, which means because of inflates him in price changes. The value of the dollar and 40 years is worth less than the value of the dollar in 20 years, which is worth less than the value of the dollar today. So Part B then ask this if the interest rate changes to 7% plus the present value of each bond, which bonds changed the most, they were going to be using the same formulas and for buying any. It's $8,000 over one class 0.7 now to the power of 20 and this equals 2,000 and $67. And for bomb be. It's $8,000 over one last point of seven Power 40 and this is 537 so we can see that the 20 year bond is still worth more than the 40 year bond there. Now, which value has changed the mouth that this is just a simple percentage change from divinity bond. A. First they'll live the 2,067 minus the value of the interest rate in 3.5% which is 4,000 and 20 divided by 4,000 and 20. And this equals it's a minus 48.5% change for bond being I was getting the same thing 537 minus 1,000 and 20 over 2,020 equals minus 0.735 or minus 73.5%. So we see that the 40 year bond is more sensitive. The decrease in the prices Graydon the last part. It says to complete the sentence. That's in the question. The sentence is the value of a bond blanked 20. Interest rate increases and bonds with a larger maturity are blank, sensitive to change in the interest rate. Then, looking back to parts and B, we see that the value of bond decreases with the interest rate receded. The present value of the bonds, or higher to 3.5% rake and they are 7% rate. And that bomb, the longer maturity, are more sensitive. The 40 year bond decreases and price more when the interest rate increases from 40 3.5% to 70% of the 20 year Von Death. This was Chapter 27 problem three.