Treasury bills have a fixed face value (say, $1,000) and pay interest by selling at a 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 inter- est over its life. The interest rate on the bill is there- fore $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. S uppose, instead, that the price rises to $975. What is the interest rate now? c. (More difficult) Now generalize this example. Let P be the price of the bill and r be the interest rate. Develop an algebraic 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.
1 answer:
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Answer:
Bond Price = $875.6574005 rounded off to $875.66
Explanation:
To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is an annual bond, the coupon payment, number of periods and annual YTM will be,
Coupon Payment (C) = 1,000 * 0.05 = $50
Total periods (n) = 3
r or YTM = 0.10
The formula to calculate the price of the bonds today is attached.
Bond Price = 50 * [( 1 - (1+0.10)^-3) / 0.10] + 1000 / (1+0.10)^3
Bond Price = $875.6574005 rounded off to $875.66
Answer:
growth rate is 0.9%
Explanation:
given data
time = 10 year
present value = $4.50
future value = $4.92
to find out
growth rate
solution
we will apply here future value formula that is
future value = present value × ......1
here r is growth rate and t is time
put here value in equation 1
future value = present value ×
4.92 = 4.50 ×
= 1.009
r = 1.009 -1
r = 0.9 %
so growth rate is 0.9%