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What are the $1-, 2-, 3-, 4-,$ and 5 -year zero-coupon bond prices implied by the two trees?...

Question

What are the $1-, 2-, 3-, 4-,$ and 5 -year zero-coupon bond prices implied by the two trees?

What are the $1-, 2-, 3-, 4-,$ and 5 -year zero-coupon bond prices implied by the two trees?



Answers

Bond A pays $\$$8,000 in 20 years. Bond B pays $\$$8,000 in 40 years. (To keep things simple, assume these are zero-coupon bonds, which means the $\$$8,000 is the only payment the bondholder receives.)

a. If the interest rate is 3.5 percent, what is the value of each bond today? Which bond is worth more? Why? ($Hint$: You can use a calculator, but the rule of 70 should make the calculation easy.)

b. If the interest rate increases to 7 percent, what is the value of each bond? Which bond has a larger $percentage$ change in value?

c. Based on the example above, complete the two blanks in this sentence: "The value of a bond
[rises/falls] when the interest rate increases, and bonds with a longer time to maturity are
[more/less] sensitive to changes in the interest rate."

Here. We want to determine the in value of a bond. Suppose we deposit $10,000 with 5% interest. Compounded quarterly for five years. For this, we will need a formula to find it. And value will be a whole Pete the parents want. Plus, I'd to attend. Where? Eyes. The interest rate for period. So here 5% is in a decimal zero points. You're five. So, um, since this is compounded quarterly with have the interest rate, hair, pig, their interest, period, eso is gonna be divided by the four. Since we have 4/4 in one year and this gives us 0.125 Ah, then. And here is the number off consecutive interest periods. So seize, um, this is compounded quarterly. For five years, we have five times, four years. So this gives us, um, so five times four. He's just 20. Um, b is them amount. Maybe I should use heart are here. So we departed $10,000 we will have $10,000 times one plus 0.125 to need. We can plug this into a calculator and run to two decimal places and we get the amount well, a 20.37. So this is the mounting donors after five years.

Okay, so you put $10,000 in a bond, pays an interest rate of zero point your seven compounded quarterly. Great. And it is for five years, so that's five times four quarters in a year since 20 periods. Okay, so here. What do we have after five years? Well, we're just going to have one plus 0.0 7/4 to the 20. So every period we get a factor of this interest rate and we get at the end of this five years are bonds worth $14,147.78.

We want to determine the value of a bond off $10,000 with 11% interest compounded quarterly for five years. For this, we will use the form now to find and value A A is gonna be equal to three times one plus I to end where eyes The interest raper period. So here, 12 11% as it does see Molly's left on over 100 0 point. So I issue a 0.11 and this is the interest rate pair period. 11% is the annual interest rate, and this is compounded quarterly. So we have 4/4 in one year. That means with you, bye bye poor here to get eye. And that gives us on the value we need to plug in here. And then we also have end and it is the number of consecutive interest periods. So since this is compounded card quarterly for five years, we have four times for consecutive interest periods. This gives us 20 and we can plug in the values 10,000 times one plus you know, 10.11 divided by four to 20 and then years a calculator. We around two to Destin moms. Ah, so this is gonna be 17 to 4 point 28th. So this is the end value of the bond in dollars.

All right now it but ten thousand dollars in a bond. Today's thirteen percent abounded quarterly said about it by four and again over five years. Twenty a compound periods. So we have done times one plus syrup on one, three, four, two, two twenty. And so after five years, our bond will be worth eighteen thousand nine hundred fifty dollars in thirty eight cents.


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