Determine The Modified Duration Or Volatility Of A Growing Perpetuity.

Question 1

Question 2

Was Galileo part of the Italian Renaissance? Galileo: Galileo (1564-1642) was an Italian scientist who helped found observational astronomy and got into trouble with the Catholic Church after supposedly defaming the Pope in one of his works. This led to him being driven into house arrest, and there he stayed for the rest of his life.
Question 3

Were the Carthaginians in Sicily? Military Technology: The trireme was a war ship used by both the Romans and Carthaginians during the First Punic War. When the Romans figured out how to build triremes and use them, the balance of power in the war shifted to their favor.
Question 4

What did the Romans gain after defeating Carthage? Neighboring Powers: After the Punic Wars, the Romans became the most powerful state in the western Mediterranean. The series of wars was inevitable as the two powers in the region expanded up against each other.
Answer to question 1

Let us first determine Macaulay Durarion as

1v(1) + 2v^2(2) + 3v^3(3)…

Let us call Sum as S, and multiply by v, so we have

(1-v)S = v + 3v^2 + 5v^3…

Here v = (1+8%)^ (-1)

THe RHS of this equation can be solved using P,Q formula, or by arithemiatci sums to get Macaulay Duration as26.

Modified Duration – MacCaulay Duration x V

So, modified duration = 26/1.08 = 24.07 or 24 years

Answer to question 2

Answer and Explanation: Galileo was part of the scientific portion of the Italian Renaissance and has become a figure emblematic of the innovations in our understanding of the universe produced during the 16th century. He was part of a growing scientific community that challenged old wisdom and was at times supported in this by the Church, but at times fervently and relentlessly opposed. These tensions defined his life and his legacy.
Answer to question 3

Answer and Explanation: The Phoenicians, from whom the Carthaginians received their culture, established trade posts in Sicily dating back to 900 BC. Centuries later, Greek colonists tried to take over the island of Sicily, but the Carthaginians resisted this movement. By the 6th century BC, the Carthaginians established control over much of Sicily. They also dominated trade throughout the western Mediterranean. The famous Punic Wars began when the fledgeling Roman Republic began expanding south through Italy and into Sicily. The First Punic War (264 BC – 241 BC) was fought by the Romans and Carthaginians and Romans over Sicily. The Carthaginians held the upper hand in the war due to their naval supremacy. However, when the Romans were able to reverse engineer a wrecked Carthaginian ship, the balance of power shifted to the Romans. Rome ultimately won the war and gained Sicily as a result.
Answer to question 4

Answer and Explanation: After the Punic Wars, the Romans gained control of much of the western Mediterranean. After the First Punic War, the Romans gained control of Sicily and other islands. After the Second Punic War, they gained control over Carthaginian holdings in Iberia and some portions of North Africa. Then, after the Third Punic War, Rome took over the remaining African holdings of Carthage. In order to ensure that Carthage was never resettled, the Romans ordered more of the city be destroyed and turned the ruins into public land. They also salted the earth to harm potential crop growth in the future.

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