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Anika [276]
2 years ago
8

You are considering buying a 30-year U.S. Treasury bond but are nervous about the effect on bond price if the yield to maturity

on the bond increases. The bond has a 3% coupon rate and pays coupons semi-annually. The duration is 19 years. Suppose that interest rates on this bond rise by 0.9%. Calculate the corresponding percentage change in the price of the bond using the approximation method based on bond duration.
Mathematics
1 answer:
Savatey [412]2 years ago
7 0

Answer:

The corresponding change in bond price = 17.1%

Step-by-step explanation:

In this question, we are interested in calculating the percentage change in the bond price using the approximation method based on bond duration;

Mathematically;

% change in bond price = Duration * Change in yield

From the question;

Duration = 19 years

Change in yield = 0.9%

Thus;

% change in bond price = 19 * 0.9% = 17.1%

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Mark and ann together were allocated n boxes of cookies to sell for a club project. mark sold 10 boxes less than n and ann sold
Lady bird [3.3K]
<span>n = 11<span>.

Explanation:
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Since Mark sells 10 less than n, m = n-10. Since Ann sells 2 less than n, a = n-2.

Together, they sold n-10+n-2=2n-12 boxes.

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The maximum value of 12 sin 0-9 sin²0 is: -​
jeka57 [31]

Answer:

4

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be \theta rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

f(\theta) = 12sin(\theta) - 9 sin^2(\theta)

Taking the first derivative of this with respect to \theta and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of f(\theta) w.r.t \theta is

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And setting this = 0 gives

12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0

Eliminating cos(\theta) on both sides and solving for sin(\theta) gives us

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Plugging this value of sin(\theta) into the original equation gives us

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This is the maximum value that the function can acquire. The attached graph shows this as correct

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