What is the duration of a three-year Treasury bond with a 13 percent semiannual coupon selling at par

the formula to calculate modified duration of bonds:

modified duration = [1 - (1 + y)⁻ⁿ] / y

since this bond pays semiannual interest,

modified duration = [1 - (1 + 6.5%)⁻⁶] / 6.5%

modified duration = (1 - 1.065⁻⁶) / 6.5% = 4.841 semiannual periods

modified duration in years = 4.841 / 2 = 2.4205 years

if you want to determine the Macaulay duration = modified duration x (1 + yield) = 2.4205 years x 1.065 = 2.5778 years

b. a single paragraph.

a paragraph is a series of sentences that are organized and make sense, and are all related to a single topic . almost every piece of writing you do that is longer than a few sentences should be organized into paragraphs. this is because paragraphs show a reader where the subdivisions of an essay begin and end, and thus the reader see the organization of the essay into subjects in order to be able to understand its main points.