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Q1- Treasury bills have a fixed face calue (say,$ 1,000) and pay interest by selling at discount. For example, if a one-year bill with a $1,000 face value sells today for $950, it will pay $...

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Q1- Treasury bills have a fixed face calue (say,$ 1,000) and pay interest by selling at discount. For example, if a one-year bill with a $1,000 face value sells today for $950, it will pay $ XXXXXXXXXX=$50 in interest over its life. The interest rate on the bill is therefore $50/$950=0.0526, or 5.26 percent. a- Suppose the price of the Treasury bill falls to $925. What happens to the interest rate? B- Suppose, instead, that the price rises to $975. What is the interest rate now? C- Now generalized this example. Let P be the price of the bill and r be the interest rate.
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Answered Same Day Dec 21, 2021

Solution

Robert answered on Dec 21 2021
119 Votes
Economics 104-402
Q1- Treasury bills have a fixed face calue (say,$ 1,000) and pay interest by selling at discount. For example, if a one-year bill with a $1,000 face value sells today for $950, it will pay $1.000-950=$50 in interest over its life. The interest rate on the bill is therefore $50/$950=0.0526, or 5.26 percent.
a- Suppose the price of the Treasury bill falls to $925.  What happens to the interest rate?
It will pay $1.000-925=$75 in interest over its life. The interest rate on the bill is therefore $75/$925=0.08108, or 8.108 %.
The rate rises as price falls
B- Suppose, instead, that the price rises to $975. What is the interest rate now?
It will pay $1.000-875=$25 in interest over its life. The interest rate on the bill is therefore $25/$975=0.025641, or 2.5641%.
C- Now generalized this example. Let P be the price of the bill and r be the interest rate. Develop an alge
aic formula expressing r in terms of P. ( Hint: The interest earned is $1,000- P. What is the percentage interest rate?) Show that this formula illustrates the point made in the text: Higher bond prices mean lower interest rates.
% rate = r = (1000 –P)/P
=[1000/P]- 1
Q2- consider an economy in which government purchases, taxes, and net exports are all zero. The consumption function is
                C=300 + 0.75Y
And investment spending (I) depends on the rate of...
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